I'm aware of the problems of MAPE as a measurement, and particularly it's uselessness in the event of a time series where 0 is one of the many values of y.
The downside to ditching MAPE in favour of something like RMSE is that that measurement is less comparable where the 'scale' of the y values involved changes. For example with MAPE I can look at model A, where sum(y) = 1000 and model B where sum(y) = 1000000 and say they're comparable when MAPE = 0.1 for both. With RMSE, an error of 100 for A vs 100000 for B makes it less clear.
What alternative evaluation metrics retain that comparability, but don't have the same problems as MAPE (particularly the inability to handle y=0)? My instinct is something like RMSE / mean of y, but I'm not certain whether that's particularly valid.
EDIT: Turns out yes, it is. It's called normalised root mean square error. I'd love to hear of any others though