Looking at BMO's back, there is a vent, a battery slot and VHS tape slot. My question is how are the AA batteries longer than a VHS tape? I doubt that magic changed the size of batteries which are AA according to the wiki. Finn is a human and the VHS tape looks pretty big in his hand so the VHS can't be small. And sure there are nukes much smaller than most nukes but it's conceivable that they were built to be portable. However AA batteries have a set size. Is this just an error on the part of the creators or is there a good explanation for it?
BMO's scale is indeed portrayed inconsistently. You may also want to note that there's an image of his innards that has no possible space for a battery pack (or video deck) and that on several occasions, his back plate appears to be secured with either screws or pull tabs and in Lost, he has no video slot at all.
What you're witnessing is the "rule of funny" in operation, where continuity takes a back seat when there's a need to introduce a joke.
The creator, Pendleton Ward has never made any secret of the fact that while plot continuity is very important to him, internal consistency is something he's happy to play with if it gets the bigger laugh:
He added that D&D is also an influence on the show’s overarching plotlines. “Continuity is important to me because I play D&D. I like having that loot. I want them to have that loot.” Aside from that, Ward said, “We just write to make ourselves laugh. I think that’s all you can do.”