As a player I can move my tile to where it needs to go and it will end up in the correct spot. I also note to the GM when I moved through provoking an AOO. Likewise I don't have to wait for the GM to update things.
As a GM it saves an enormous amount of time, quite often sorting out the tools and posting up the snapshots is significantly longer tan any other aspect. I'd place map jiggling as taking up about 60% of my PbP GMing time.
Downside is that players can shift about as you say and a few things get missed.
On balance I'll take the speed over possible lack of accuracy, but then I like fast paced storylines and fast paced combat - a PFS Scenario to take no longer than 4 weeks, which means combats need to take 3 days at the absolute MAXIMUM regardless of level