Inverter Voltage Control - Stability Concerns
In answer to your second question (which is the easiest), your 5% scheme produces a system which is almost guaranteed to display a certain degree of instability. Let's say that (just as an example) a duty cycle of  50% gives a slightly low output, and 52.5% (1.05 times 50) gives a slightly high output. Then the system will "hunt", shifting back and forth between the two duty cycles. This is a classic problem with feedback systems with quantized outputs. The solution is also classic - establish a "dead zone" in which small errors around the desired output are ignored. Generally the dead zone must be equal or greater than twice the output quantization; in your example, +/- 5%.

The first question is a little harder, since it depends on how much error you can tolerate. A proportional controller provides an error proportional to the inverse of the feedback gain - the higher the gain, the less the error. In principle this error can be made arbitrarily small by increasing the gain. However, since there is always delay around such a loop (in this case the obvious one being the rectification and filtering of the output of the feedback transformer, but the filtering required to remove harmonics from the bridge output also counts), at some point increasing gain will cause the loop to become grossly unstable. If this limit is reached while the error is too large, more sophisticated measures are called for. This is also a classic problem, and you are aware of the classic solution - a PID controller. As to whether or not you need this solution - well, that's up to you. There's no way anybody can tell without a detailed system analysis.