Mouse,
There are a couple of waterfalls on the way up, at one point it's good size. Those look to be good spots. There is also Lone Pine and Mirror Lakes then finally Consultation Lake near Trail Camp. The pond at Trail Camp is not a good place since there are so many campers.
And there is a nice running spring on the lower switchbacks. That would be the last source, and first source on the way back from the summit.
As for filtering that is personal choice. If unsure take water from running sources rather than lakes, and are upstream from campsites.
Have fun, it's awesome up there right now!
James