Hello, I hope the following assists you.
If during any service defects are noted by the technician then these defects will be noted on the invoice to yourself and also on the companies own computer system. The company does this as if there is a defect with the car that is reported and this defect should cause an accident or injury they can't be held legally liable. Obviously this works the other way, if a defect is missed and it causes an accident or injury you are able to return to the company and hold them liable as you would have had the defect repaired if you knew about it.
The extent of what is recorded that is available to other people depends on where the car is serviced, most franchise dealers record the work carried out and reported with the manufacturer but this is a recent development, independent garages will have a record of their own which wouldn't be available in general unless specifically requested with a genuine reason such as a prospective purchaser checking on the vehicles history with the owners permission.
If a car still has a valid MOT even if another MOT was carried out which revealed defects the original MOT remains valid.
I hope this answers your question but if I can advise further let me know and I'll reply as soon as I'm able to.