Talking about basic equipment might seem pretty fundamental to some of you, but you'd be surprised how many ropers of all levels I see at ropings and schools with basic equipment breakdowns. Whether it's a saddle that doesn't fit a horse's back and is therefore affecting his performance, or something as simple as a loose cinch, people need to take care in getting the right equipment in the first place, then maintaining it and adjusting it correctly. It's a matter of both safety and success.
Being cautious when you're tying up your horse is really important, so you don't get your fingers tangled up in the reins or the lead rope in case your horse sets back. I've had friends lose fingers that way. It happens, so don't loop your reins around your hand or fingers when you're just sitting around, either.
Make sure the hobble between your front and back cinch is strong and adjusted to the right length. If that breaks or is too long, your horse is flanked and might want to buck you off. That can happen at the worst times if you don't pay attention and prevent it from happening.
I'm a firm believer in a tiedown, because without one a horse is liable to throw his head in the air. Then you can lose control and get off-balance. A horse with rate is fine in a leather-nosed tiedown. A chargy horse might need a harder tiedown with a covered rope noseband. One size definitely does not fit all horses when it comes to equipment and how it's adjusted.
Constantly check the Chicago screws in your headstall to be sure they haven't loosened up or one of them hasn't worked its way out. You can put Super Glue in there to keep that from happening. Imagine your horror if you go to pull on your horse during a high-speed run and the bridle comes off. You're really sunk if that happens.
A lot of times I use the same bit on different horses. So I need to be sure the bit's in the proper place in each horse's mouth. You need to have the chin strap properly adjusted also. If equipment isn't adjusted correctly, it doesn't function properly. You might be getting after your horse, but the problems might not be his fault. It might be the equipment adjustment.