In recent weeks, I notice that when I put my car in reverse first thing in the morning, it judders. The vibration stops when I shift to other gears. It also does not happen when the car is warmed up. Do you think there is a problem? If so, how serious is it? The transmission is a four-speed automatic.
The first thing to do is check the car's transmission fluid level. Follow the instructions in the owner's manual on how to do this. If the fluid level is low, topping up with the exact recommended transmission fluid will most likely solve the problem. However, a low level usually means there is a small leak which may not be easily detected and this must be fixed.
In any case, you should have a transmission shop drain the existing fluid, replace the filter and then replenish with new automatic transmission fluid. This is an often forgotten maintenance routine.
Transmission fluid deteriorates over time and this severely reduces gearbox performance.
If the judder persists, check engine and gearbox mountings which, if broken, will also give rise to judder when either forward or reverse is selected.
If the problem persists after doing all of the above, a transmission overhaul may be the only course of action. This is expensive but recommended if the rest of the car is in good shape and you intend to keep it.