Back in the day, Access had page level locking only. In a nutshell, this
could cause more than one record to be locked in a table if the records were
under 2K in size.

Newer versions have the option of record level locking ensures only one
record is locked when someone is modifying it in a form. There is a slight
performance hit but well work it.

If you do not have record level locking selected, it's possible that someone
could be working on another record in a table yet still lock your record. I
would check it in both the FE and BE; however, I think that it really only
matters in the BE.

However I doubt that this is the cause of your problems. The first thing to
check is if ALL users have full permissions to not just the database files on
the network, but also the entire folder which holds the database files. If
you can't create, delete, edit files in that folder, this could lock you out
of a record as the .ldb file (which keeps track of record locking) can't be
properly updated.

The next thing to check is to see if you have code or queries that lock an
entire table.