Cold water pressure poor in shower. Just had Rheem installed.

If cold water has good pressure, and you are not on a well ,try turning water Off to water heater,open tap to relieve pressure remove hot side left water line to heater stick long screw driver inside pipe going inside water ,the heat trap is sticking it's rubber flap inside the pipe going in water heater.

It *may* not be a problem with the water heater itself necessarily. When you say "keep adjusting the water temperature when you're taking a shower" I presume you're talking about turning the shower hot/cold knob(s) and not the temp thermostat on the water heater itself.
If so, when it starts to run colder, turn the knob all the way to full hot. Is the water then very hot? If so, the water heater is working fine & doing its job, and the problem is likely to be in the shower faucet mixing valve itself. Sometimes a faulty one will expand the inner seals/cartridge as hot water flows thru it, and starts to (wrongly) restrict the hot water flow, thus causing the constant need to "turn the dial up a notch".

http://waterheatertimer.org/Low-hot-water-pressure.html

Gene
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If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Which type Richmond water heater?
Is this a tankless water heater or tank-type?

Tankless are notorious for 'cold water sandwich' under exact conditions you describe. You might need tankless with larger BTU burner.
Don't install a tankless.
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html

If you have tank-type water heater, then I suspect a clog in the hot water line, or single-handle faucet cartridge in show is going bad.
Same problems can contribute to tankless problems.
http://waterheatertimer.org/Low-hot-water-pressure.html

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Rheem makes a number of tankless models
http://www.rheem.com/products/tankless_water_heaters/

They make a tankless 95 outdoor series
http://www.rheem.com/product.aspx?id=EBA80FAA-3C0F-411D-AF83-82061C28ED1B

The 95 outdoor series spec sheet says .4 GPM minimum activation and .26 GPM flow to keep burner activated. The colder the incoming water, fewer users can take a shower at once.
http://globalimageserver.com/fetchDocument.aspx?id=ea5f0816-dfd4-4bcf-a605-79945619f5bb
The .4 GPM and .26GPM numbers are fairly typical for tankless units.
These numbers are good when the unit is new.
After a few years the number may be different because the tankless is a high-tech machine with sensors that are susceptible to particulate in the water, and susceptible to perfect-functioning of other parts in the machine.
The outdoor series spec sheet says the tankless is good to minus 30 F.
But remember that's when the unit is new.
Outdoor tankless water heaters have an electric heater that keeps water pipes inside the unit from freezing, as long as electricity is ON.
If electricity goes off, the house stays warm inside for several hours.
But a steel box located outside would get cold immediately without electric heat.
The electric heater adds standby cost to operational expense.
The tankless has a heater, but you still have to protect the incoming and outgoing pipes.
If your incoming water is very cold, the tankless heater may not be able raise the temperature fast enough to give two showers -or- even 1 shower depending on age and efficiency and capacity.
You can add a tempering tank located in naturally warm area that passively pre-heats incoming water before it enters the tankless burner.
It might be best to locate tankless inside the house >> and use direct vent through the wall for both incoming air supply and outgoing vent gas.
If incoming air is taken directly from the living space, then tankless will draw air into the house through cracks and around doors.
A lack of sufficient air, or poor air quality can cause the burner to shut down.

When buying a tankless, read the spec sheets and really ask questions about everything you don't understand.

your cold water supply check pressure

How long has the heater been installed?

there is a little cap on the hot and cold side above the shut off valves, turn the water off at these valve and take the caps off there are filters in there clean them off and reinstall them that should take care of the problem, you might want to flush the tank while your at it hook a hose to the hot side connector and run it out side or to a sump pump then turn on the cold water and flush it out you can also reverse this procedure by doing it on the cold side

Many states building codes require a pressure regulator and expansion tank for hot water heater installation. Check the pressure regulator if you have one as this would only affect the hot water pressure. Adjust or replace. Rap the expansion tank like knocking hard on a door. Hollow sound is good. Dull thud means it needs to be replaced as it is filled with water.

Error code 13 is "oxygen depletion sensor" activated.
The first number is a sequence indicator.
If you need the training manual I have it and can send it to you.
I got Rheem to send it to me a while back and it is a big help when working with these units.
It covers th RTG-42, 53, 66 and 74.