Is "different than" incorrect grammar?

Yes, "different than" is bad grammar. The correct phrase is "different from". An amusing blog has this to say:

"A sensible discussion of different from versus different than may be found in Theodore M. Bernstein's The Careful Writer, published in 1965. Bernstein favors the former usage in most instances. So does the usage panel in my 1976 American Heritage Dictionary. The argument has nothing to do with Latin. People say different than out of the mistaken belief that different is a comparative adjective and thus takes than, as with better than, faster than, etc. But it's not a comparative (diff, differ, diffest?), it just looks like one. Different is used to draw a distinction and thus properly takes from, as do separate from, distinct from, apart from, etc. (One recognizes that we say in contrast to; one also concedes that another false comparative, other than, is firmly entrenched in the language. Never mind, this is English. One does the best one can.)"
-The Straight Dope

To summarize:
different= distinction, not comparative.
than = comparison
then = time