Definitely would have had the whole "with great power must also come..great responsibility" thing. Iirc, the show completely ignored that and Uncle Ben altogether. Peter gets his powers and decides to become a superhero...just because, i guess.
I also would have included the entire supporting cast. I have no idea why the producers decided to ignore one of the things that made the comics so great.
Would have used more villains from the comics. Even with a low budget, they could have had Chameleon, Kingpin, Silvermane, Hammerhead, Mysterio, Bigman and The Enforcers, etc.,....Hell, with a little imagination, they could have Included Green Goblin and Doc Ock. How hard would it have been to just suspend Goblin's glider in place, and have a screen behind him to simulate flying? They did that successfully with the Witch in the Wizard Of Oz 40 years before the Spidey series...Ock's tentacles could have been stop-motion or even just operated by puppeteers.
These three things were sorely missing from the 70's series, imo...