Is it common for drummers to get blisters/calluses on his or her fingers? Whenever I play on an electric drum-kit, my fingers swell up with blisters. Could this be due to bad hand form?
Don't worry about it. My fingers often get blistered, especially on my left hand. You might be gripping the sticks too hard but even if you aren't you'll might get blisters after a while. If they hurt but a band-aid on them or invest in a pair of drumming gloves which will improve grip and stop blisters.
Blisters are not good. If a blister starts to develop, it may be helpful to put a special blister bandage ("second skin") on it. But prevention would be better. Hopefully Laurence's suggestion of the technique adjustment helps. Also, you could try putting a small piece of athletic tape on the specific spot where you tend to get a blister, before you play. I would take it off afterwards, to allow for good air circulation.
About callouses. Speaking as a string player, I find it helpful to have some callous, because otherwise, playing for several hours a day can be painful. (Also, playing with not enough callous in a very humid environment makes fingers feel too sticky.)
To build up some helpful callous, I find it helpful to play at least 30 minutes a day for a week or so prior to a day when I know I'll be playing for several hours.
There are times when callouses get a little too thick, and this can interfere with sensitivity of the fingers. Also, sometimes a sharp edge of callous appears, which can snag on things. The solution to both problems is the same: gentle filing with a fine grain nail file (emory board or metal, whichever you prefer).