So there's two instances where I don't like last hitting.
1) Which should be obvious for the title is last hitting minions for gold. I don't like the mechanic at all. It favors some champions hugely over others. I would say very simply any hero that did damage to a minion when it dies gets a cut of the gold.
If a minion would yield 20 gold on death and 2 heroes hit it before it died, they each get 10 gold. If 3 heroes hit it before it died, they each get 7 gold (round up). I think this would make a much better balance for heroes that can't toss powers out just to finish 5 minions at once.
2) Now the one that probably isn't obvious for the title is last hitting heroes for a kill. I've actually hated this tactic for a long long time across many games like MMO's and FPS's. I believe the person who does the MAJORITY DAMAGE should get credit for the kill. Not just some guy who saved his power up for the last hit.
This would also alleviate people who stupidly save hard hitting powers up literally just to get credit for a kill. I've seen instances where it's a 2v1 or 3v1 situation and it's already 100% guaranteed going to be a kill just by auto attacking. But people toss out their ults just to get the credit for the kill. How stupid is this.