Account number not matching name/address

Normally nothing.

The bank will do a double verification on account number and name but almost never address. The name and account number check is for safety to ensure that if you get 1 digit wrong on entry they can identify the actual account via the name so if you send to john smith with account 111111211111 but John Smith actually has account number 111111311111 then they will sanity check the transaction.

I use online banking and it is clear that only the name - company or private individual - and account number are essential for a transaction to be processed. Any address details are optional.
Also, if I make a typo in the numbers so that the last two digits don't 'check' with the remainder, I get a warning to confirm that the details are correct or the transaction will be rejected.

Your question isn't sufficiently clear. Are you paying for something, or being paid for something?

If you are paying for something, then be very careful. e.g. you go to a shop and buy something, or take a service from a company, but pay the private account of one of the employees, technically the business hasn't sold you anything.