Excess would be the point where the board manufacturer replies saying it will cost extra to produce your PCB, as it costs them machine time drilling all those holes,
You can get pretty over the top with the number before they complain, (about 1200 on a 10x10cm 2 layer board from memory) avoid the minimum size, the smaller drill sizes break more frequently, and have a slower depth drilled per second which takes longer, so instead of a 0.3mm hole in your via, make it a 0.5mm hole and there will be much less friction, the larger the better if you don't need it tiny.
Other side effects on a circuit level is, well the hole is not as conductive as the trace, so you increase the resistance of any trace you shotgun spray with vias,
Other things can be a sort of tear along the dotted line problem, a rectangular PCB will normally curve when flexed evenly over the entire length, if you have rows of vias all in a line, that area will flex more than the rest of the PCB, and may be subjected to higher stress than the rest of the board,