I'm too lazy to rewrite up my thoughts on this episode, so I'll just paste some earlier comments (with a few added thoughts) on why, despite its fair share of enjoyable enough moments, its ranks among the weaker of the classic era episodes:
Burns' Heir seems to be the first episode that anticipates the numerous problems that were to reoccur during the double-digit seasons, namely an unrealistic and often silly storyline, a number of gags gratuitous to the plot (Homer as chimney sweep, the boot kicking Bart, Homer repeatedly kissing Hans Moleman, his flower addiction, the Orange Julius) or just plain disturbing and/or tasteless (the exploding head, Burns' rib cracking and Bart's hunchback posture) and out-of character acting, Homer and Bart in particular. Homer isn't a jerkass like in later episodes, but there seems to be no depth to his character - his behaviour is extremely stupid or just plain weird (like calling Burns Kurns - the flowers and Hans Moleman bits have already been mentioned) - this is not the Homer we know and love, but unfortunately a one that we would suffer in much of the later seasons but with the added boorishness and mean-spiritedness from many episodes from Trash of the Titans onwards. Bart is also poorly characterised, switching uneasily in act one from an exaggerated version of his rampant destructive side (smashing windows left right and centre, knocking the heads off statues, flooding the car) through suddenly liking Burns and disliking his family in return to suddenly missing his family, making the resulting emotional conflict somewhat thin and contrived, especially as it's hard to feel much sympathy or empathy for his plight when we have no real logical explanation of why he went to live with Burns (other than Marge practically forcing him - more OOC acting), or, hell, why he was appointed heir in the first place. Finally, the bit with the actors imitating OFF (especially the Estonian midget playing Lisa) with them hanging out with the Simpsons to get their characters is probably the stupidest plot twist of the classic era, second only to the Springfield Elementary School and Prison at the end of The PTA Disbands, and is all too prophetic of many similarly (if not more) implausible plot developments that plagued so many of the later Scully episodes.
However when all's said and done, it's not bad, just too flawed to repay many repeated viewings. C+