You've forgotten about Jane Stickels, Martin, and Miss Tonks, the stewards' secretary, both of whom were stood down from duties. Tonks resumed duties a couple of years later, having gone on a remedial course. But there are other eyes and ears which are employed to look out for things like tack - the stewards are closeted in a tiny room without any sight of the horses - they view everything through multi-screens (as you'll see if you watch the programme), and they're not able to see anything the camera doesn't obviously pick up.
You have a parade ring marshall, who's supposed to check that horses are wearing the correct number cloths, the correct tack, and that jockeys mount and get onto the track on time. He also assures that horses with permission from the stewards go to post early, take a pony, or don't have to parade if they're very difficult, but can be mounted in the pre-parade (like one of Gay Kelleway's years ago - was it LUNDY'S LAD?) and go straight to post. He is supposed to spot inconsistencies with declared tack and get it put right before the horses exit the ring. If he doesn't do his job properly or, as is often the case now, there isn't a marshall due to the BHA's incessant cutbacks of jobs it deems unnecessary, it isn't the stewards' fault.
Further to the BHA's attempts to cut back on 'unnecessary' raceday jobs, they've told Lingfield to drop the starter's signaller - the man with the flag who stands to the side of the stalls and indicates to the starter when all the handlers are out of the way, horses and jockeys are ready, and it's safe to start. Lingfield has protested on H&S grounds, but the BHA says the starter can handle radio contact and such duties for himself, including indicating a false start to the false start flagman down the track. Not that in any way one wishes these things to happen, but it's probably a matter of time for something to go wrong, and the starter can blame the BHA.
Anyway, back to responsibilities for tack: you have a starter and an assistant starter, both of whom are also supposed to check for discrepancies at the start - the parade ring marshall will radio if he hasn't stopped someone in time, to say Bonzo Dog will be arriving minus his tongue-tie, for example, or with cheekpieces which aren't declared. The trainer will then be referred to the stewards for not complying with what he's declared when he signs the horse in before racing. If the horse is fitted with an item that isn't declared, it's removed; if it hasn't got on what it's declared to have on, if there's time for the groom to rush the item to the start, it will be allowed to be put on, but there's no guarantee that there still won't be a fine for additions or omissions. That's one of the duties of the declarations clerk's job - to ensure that all relevant officials know which horses are wearing what - and the duty of the trainer or his rep to ensure such information is recorded on the declarations sheet first thing before racing. It's often a question of trainers forgetting to write up their horse's tack on this, than anything sinister, which causes problems. You might, for example, be switching from blinkers to cheekpieces that day, and inadvertently still write 'blinkers' as you're so used to that horse using them. But it's up to other raceday staff to check that tack is correct, not just the trainer. The stewards just get to handle the fall-out.