What is a relevant example on the type of errors which can be made in the entries to the accounts that will not affect the balancing of the trial balance?

Entries in wrong accounts and fully omission of particular accounting entry will not affect the trial balance. 

There are two types of errors that can occur in a trial balance.

Type one errors effect the balancing where as type 2 errors don't.

Type 2 errors are.

Error of principle

Error of Commission

Error of reversal

Error of Omission.

Error of Subsidiary Entry.

Compensating Errors.