It was a 12 week course plus homework to learn how to inspect and test an electrical installation. And the failure rate for those taking the exam (C&G2391) is quite high even when the course is for electricians who already have the basics anyway.
To explain what to look for on a forum is rather a tall order.
In the main it's DIY work which is the problem so untouched there is likely not that much wrong. To bring to modern standards likely it will require a consumer unit (CU) change to get RCD protection. It should have earths to lights but at that age if may have slipped the net.
Water pipes being changed to plastic can cause problems. But likely most problems will be corrected with a CU change.
I think it is very easy to make mistakes. One of the common things is one electrician you hold in high esteem will make a statement which is for the circuit in question maybe correct but not correct for all situations.
For example "RCD protection is "required" on socket circuits now" well in essence yes but over 20A no so you could have a cooker on a 32A plug and socket without RCD protection.
The theroy and practice do not always work together. There is a special cable called Ali-tube designed to go in stud walls and it does not need RCD protection. However try and buy a short lenght and you will realise why its not used much.
The regulations say that fixed items over 2kW should have their own dedicated supply. Immersion heater always but washing machine, tumble drier, dish washer all should have dedicated supply but often just fed from a dedicated kitchen supply.
The debate on how many RCD's a house should have goes on and on. Some will say two but I have not found a single regulation that says must be two or more. I says:- 314.1 Every installation shall be divided into circuits, as necessary, to: (i) avoid hazards and minimize inconvenience in the event of a fault (ii) facilitate safe inspection, testing and maintenance (see also Section 537) (iii) take account of danger that may arise from the failure of a single circuit such as a lighting circuit (iv) reduce the possibility of unwanted tripping of RCDs due to excessive protective conductor currents produced by equipment in normal operation (v) mitigate the effects of electromagnetic interferences (EMI) (vi) prevent the indirect energizing of a circuit intended to be isolated.
Which has been interrupted to mean at least two RCD's. The RCBO (That's a RCD and MCB in one device) if often single pole switching and as such one questions if they should be used on TT systems. Also although it may "minimize inconvenience in the event of a fault" it can also go unnoticed and losing supply to fridge or freezer could be dangerous to ones health.
I would say the RCD question is the big one as far as a re-wire goes. RCBO would seem the best but also not all RCD's are the same. The X-Pole RCD for example has a monitor built in and is also less likely to trip due to electrical storms. There are even auto-resetting RCD's but at £350 each not normally fitted on domestic premises.
The Electrical Safety Council do a series of "Best Practice Guides" look at No 4 Issue 3 and No 1 issue 2. Then you may have further questions.