Your shutter is probably used up to its designed lifecycle. I have the same problem of shutter being slower than what the setting shows, which definitely leads to over exposure. I have to switch to continuous shooting mode (either H or L) to try more frames to get it back to the correct speed. Somehow the problem pops up again and gets worse through time. I guess I've clicked it for over 100,000 times over the last 7 years since I bought it. Aging was what my photographer friend suspected. Will check out.
I'm using a 17-55mm f2.8 lens as standard fitting , perfect for DX format and so far extremely rarely does focus error occur.