Back in the mid 90's there was a guy around here who actually opened a school and he went around bragging about his "self taught" ability and how he always "schooled" the black belts when he visited the local schools....yes none of us ever heard nor met this guy.
I went to his school and invited him to a tournament and listened to his speel about how great he was. He was so full of crap and it was obvious he didn't know anything but some sloppy karate moves when I watched his class...which he would not let me participate in for some reason.
A month later he showed up to the tournament and entered to fight. He had his five students there. He fought one of my black belts who seriously owned him and embarassed him (intentionally). He never opened his school again after that.
Video training is a great resource if you have actual training but one cannot learn something as complicated as Karate without guidance from a qualified instructor...but now a days you need to be really picky on which dojo you join and make sure it is an authentic system with a truly qualified instructor instead of some commercial mcdojo. Good luck.
You'll get the basic kicks and punches down, but you might commit mistakes with certain moves. This might result in injury or lack of power in the maneuver.
You also need opponents to spar against to properly learn how to defend and launch attacks.
If you just want karate as a form of exercise then I guess a DVD would be fine, but if you want it for self-defense and to properly master the art then you do need to go to a school.
No you really can't.... I good instructor is essential. Its the only way to learn it. From a DVD you can't ask questions and or get corrections and tips.