If an alternator is intermittantly going out can this cause the engine to misfire

What year is your Altezza? Misfires can be caused by a a few different things. Spark, Fuel and Compression. When I check for these I go through a set list of checks so I might suggest stuff you've already tried.
Have you had the vehicle scanned for OBD Trouble Codes? These will give clues to where the issue could be and if it is a sensor problem. If you get codes comment below with them and I'll try to help explain them.
Do you know if it is a single cylinder or a multiple cylinder misfire? A single misfire could be the spark plug or the coil pack firing it. A multiple misfire could be a faulty sensor.
Next check the fuel system, A 'sticky' or worn injector can cause regular and intermittent misfires.
Next your check for vacuum leaks.
Check the Mass Air Flow sensor as this can get dirty but this often throws a trouble code and turns on the check engine light.
If it is a single cylinder misfire there are simple tests you can try. Let me know the year and engine size of your Altezza and I'll try to help you more.

parts costs for any car , on earth are not the same all over earth
not even close, .
unless in N,Korea or Cuba.
new, used , rebuilt
beside the mount error
all those error could be just 1.
even vacuum leak.
P0300 says all cylinders misfire so there other P030x error are pure redundant.
cam sensor is serious, in the real world that cam sensor error is very serious. and causes misfire, so misfire is expected

why add up cost when you've no clue what is bad.
OBD2 DTC are just the starting point of diagnosis
the PCM is not AI, not by a country mile ,even to the moon.

we cant watch you or the car ( in the secret act)

did you crank a dead engine so LONG, that battery went low and now all computers in the car are telling lies, and is common as nails now. this effect..
no symptoms told at all just a DTC dump.
no engine told at all and A4
4.2 L V8 40v DOHC >< complex this.
seems it is just 1,
posted ANON so no other way to know what engine is here.
nor there post full of symtoms not told here
and what happened the day this all started.
engine died? what?
starter cranking slow is not good,
step 1 on all cars , we keep the battery fully charged till the engine starts to run and stays running and battery volts are 13 to 15vdc,
a volt meter tool find that easy.
if below 13vdc the alternator is dead or its fuses.blown.


also we do not sell engine parts. here. just free advice ,just that.
no miles on the car told, over 90,000 miles
and the silly cam belt failed. making CAM sensor go dead?
the belted cams can not be ignored
the belts are changed out at 90k miles 140km
https://www.rockauto.com/en/catalog/audi,2005,s4,4.2l+v8,1430752,engine,timing+belt+&+component+kit,5759


good luck , DTC codes are not AI, not at all

Change #2 coil with #3 and see if #2 runs good.Now if the code comes up with #3 misfire you know you just need a coil and that is most likely what it is going to be if you go with the odds of causes of a misfire on that engine..

First thing, fix leaking exhaust, this can cause erratic idling...second thing, remove and clean IAC valve and MAF sensor..dry and replace, also try putting some SeaFoam in the petrol, engine oil and air intake, let sit for 10 minutes then go for 10-15 min drive...suggest you change engine oil shortly after driving about 5000kms, if the oil is old..

Did you get any codes on the misfire? If you did not, test ignition coils, test vacuum, test fuel injectors, verify correct plugs..That's right, anything from a fouled spark-plugs to burned cylinder head valves can cause a misfire. Whatever the root cause of the misfire, the bottom line is that one or more cylinders are not contributing to total engine power output. This leads to power loss, rough idle, unstable RPM and bad gas mileage...cheers

Diagnose Engine Misfire - Auto Diagnosis Repair Help

www.aa1car.com/library/misfire.htm

The engine may shake so badly at idle that it causes vibrations that can be felt in ...The engine may only misfire and run rough when cold but then smooth out as ...

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Jun 27, 2013 - NOTE: You MUST restart the engine for the misfire to go away. ... in an expert to do that test, but it might be worth it to prove/disprove the injectors being thecause. 0 ... The first is that the car should run fine even on cold starts.

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Mar 24, 2009 - They also gave it to me because of this misfire problem it has. ...Engine misfires when cold but runs fine after warming up few minutes later? ... and you start next morning will also cause a misfire until it burns off the coolant.

"Miss/splutter" with cold engine, but fine when warm? M103 / also ...

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Jul 13, 2011 - My moms old 300SEL (with the M103) that was once my car is now my "work car" again as she is getting a brand new SUV very soon.

Cold start misfire solved (finally!) - Bimmerforums

P1633 means the battery was disconnected or became discharged enough to be unable to keep the battery-backed memory in the control module alive.

If the alternator is failing intermittently, it may not always keep the battery charged enough to properly run the engine, which could cause misfires. Ensure the battery and its terminal connections are in good shape.

I am trying to connect the two facts you listed. Your facts may not be enough to find the actual cause of the misfire, however. Certainly a disconnected or otherwise discharged battery will cause the P1633 code.

Trouble Code: P0304 (2.0L L4 VIN C Auto)
Cylinder 1-4 Misfire Detected

Trouble Code Conditions:
Any time engine is running and the Target Learning Coefficient has been successfully updated. When more than 1.0% misfire rate is measured during 2 trips.

Possible Causes:

• Intermittent misfire
  
• Base engine or ignition system problem
  

Misfire is a common driveability problem that may or may not be easy to diagnose, depending on the cause. A misfiring cylinder in a four-cylinder engine is, pardon the pun, hard to miss. The loss of 25% of the engine's power output is the equivalent of a horse trying to run on three legs. The engine may shake so badly at idle that it causes vibrations that can be felt in the steering wheel and throughout the vehicle. The engine also may be hard to start and may even stall at idle, depending on the accessory load (air conditioning, headlights and electric rear defroster, for example).

When misfire occurs, performance suffers along with fuel economy, emissions and idle quality. And, when a misfiring vehicle is subjected to an emissions test, it will usually fail because of the unusually high levels of hydrocarbons (HC) in the exhaust.

What causes a cylinder to misfire? Basically, it's one of three things: loss of spark; the air/fuel mixture is too far out of balance to ignite; or loss of compression. Loss of spark includes anything that prevents coil voltage from jumping the electrode gap at the end of the spark plug. Causes include worn, fouled or damaged spark plugs, bad spark plug wires or even a cracked distributor cap. A weak coil or excessive rotor gas inside a distributor would affect all cylinders, not just a single cylinder.

"Lean misfire" can occur when the air/fuel mixture is too lean (not enough gasoline in the mixture) to burn. This can be caused by a dirty, clogged or inoperative fuel injector; air leaks; or low fuel pressure because of a weak pump, restricted filter or leaky pressure regulator. Low fuel pressure would affect all cylinders rather than an individual cylinder, as would most air leaks. A leaky EGR valve can also have the same effect as an air leak.

Loss of compression means the cylinder loses most of its air/fuel mixture before it can be ignited. The most likely causes here are a leaky (burned) exhaust valve or a blown head gasket. If two adjacent cylinders are misfiring, it's likely the head gasket between them has failed. Also, if an engine is overheating or losing coolant, it's likely the head gasket is the culprit.

Intermittent misfires are the worst kind to diagnose because the misfire comes and goes depending on engine load or operating conditions. They seem to occur for no apparent reason. The engine may only misfire and run rough when cold but then smooth out as it warms up. Or, it may start and idle fine but then misfire or hesitate when it comes under load. Also, it may run fine most of the time but suddenly misfire or cut out for no apparent reason. Intermittent misfires can be a real challenge to diagnose, so let's start with a steady misfire in one cylinder before moving on to intermittent misfires.

Hope this help.

When cleaning your engine, water/degreaser went down the spark plug ports. Try using a air compressor blow gun to remove the moisture from around the spark plugs and boots. The water was causing the engine to misfire on 3 cylinders at first and as the ports started to evaporate the moisture, the less misfiring was occuring. Dry thouroughly and hopefully coils do not have damage to them. Also check to make sure the boot is making good contact with the spark plug.

How's your coolant level? The intake manifolds on the 3.8L engines are prone to breakage at various locations causing coolant leaks into the crankcase and vacuum leaks on intake ports.Removal of the upper intake manifold will be necessary for inspection. Also, check for vacuum leaks at various locations on the outside of the intake manifold using WD-40 or brakeclean/carburetor cleaner sprayed hoses, non-electrical components, at the base of the manifold etc. As for a faulty injector, not likely but if you suspect one you can always swap the suspect injector with another on the engine and see if the misfire follows the injector. Just be sure to relieve the fuel pressure before servicing. Hope this helps.