My zzr1200 is having a problem back firing and decrease in gas mileage along with poor cold idle. It seems like a timing problem. the bike has 75,000 miles. The valves have not been adjusted either.

symtoms of a bad coolant sensor. poor idle, stalling, rich mixture, retarded timing, low idle speed, cold hesitation or stumble, poor fuel milage. ( will also ****** timing ). in some cases you can unplug sensor and the pcm will compensate by running a default air/fuel ratio and in some cases allowing car to run without the sensor.Id just replace it !! if light is on, get vehicle scanned to find problem code. most all auto parts stores will scan for free, auto-zone etc. have a good day !!

What grade of fuel are you using? There are many conditions that effect gas mileage. The way a vehicle is driven, is it shifting correctly, flooring it to get up to speed from dead stop also known as Jack Rabbit starts, driving with the defroster on when it isn't needed or the setting just above that can be used. Back in the 90's most car manufacturers made a change to their heating.cooling system that caused the AC compressor to kick in when the selector was set to defrost. This puts drag on teh motor and decreases gas mileage. Build up on valves and low compression in the firing cylinders will cause you to lose gas mileage as well. Do a compression check on the motor to make sure you don't have abnormally high compression or low compression on cylinders and use a bottle of gas treatment in your fuel to clean some of the carbon build up from injectors and valves. Also start using the Mid grade fuel. Not the High Octane in your area. In Texas we typically have 3 choices 87, 89 and 93 to choose from. Low grade is enough to run the vehicle but performance is low as well as mileage. I use the 89 octane for better performance and better mileage. The High Octane or 93 isn't really good as it leads to higher carbon build up on the valves. Also check your oil often and make sure your changing it every 4000 miles at the longest. All of this along with making sure you change the Air Filter every 5000 miles will increase your mileage.

on average a cat will last between 5 and 10 years get a hydrocarbon readout to see if cat needs replacement.

change the air charge sensor on the back of the intake

75,000 miles for heavy urban city driving.
100,000 miles if you drive a lot of freeway.
Mix driving should be under 90,000 miles.
If your the timing guide (on the side of the timing belt cover) making noise then you should change it ASAP.
A loose timing belt will offset timing on the injector and decrease mileage.