Hello,
MS Access is a desktop relational database product based around the Jet database engine, same as Visual Basic and other Office applications (unless you go for an Access Project, which uses SQL Server or MSDE as its database and Access just provides the user interface - forms, reports, toolbars etc).
Access does indeed have the ability to run a normalised database with referential integrity and check constraints, just as you would expect in client/server products. The files can be easily backed up by copying the MDB or MDE file to another location.
You seem to be approaching this from a negative point of view, which suggests to me that you may have reasons behind wanting to change and so are therefore using this to obtain evidence to support your quest.
I am therefore going to give both sides of the story:
Access applications can be very stable and operate for years without problems, indeed many members of this forum make their living developing and supporting applications in Access.
Access is superb at quick development for small to medium size database applications, or to use it as a front end for client/server databases such as SQL Server, MySQL or Oracle.
Where it is less good is when the applications become larger. The MDB file format has a size limit of 2Gb, so if you have a lot of data - or use BLOBs to store files inside an MDB/MDE file, you will hit that limit very rapidly. If you are getting anywhere near that limit, I'd strongly advise moving to something else as a backend store anyway.
I've mentioned that the data can be backed up just by copying the MDB file - if you don't secure the data properly, a database can easily be copied by using the operating system copy command to a CD or USB flash drive, resulting in data confidentiality to your employer. This can be circumvented by using Access purely as a frontend to a client/server database so the data are not stored within an MDB file.
Finally, a pure Access database file doesn't cope well with multiple concurrent users. If you need to have lots of concurrent users on the system, then use an SQL back end to an Access frontend using unbound forms (not linked tables as this is very slow - search the forums for more information as to why).
Operating system and Office version upgrades on your client PC's shouldn't cause Access databases to stop working, provided that the version of Access you run supports the Access file format version and any features you use, plus external references to libraries have been installed on your PC.
I've been developing applications in Access since 1999 and have three in use commercially within the UK; I've also written a free addin tool to document the objects within Access. In the right hands, Access is a very capable tool with a lot of potential, but just as with any tool, it can be misused and i've seen some absolutely dire applications over the last few years.
One last piece of advice: Bear in mind that as a relatively new employee, your employer won't take kindly to messing with business critical applications without very good reasons. I strongly suggest that you search these forums, the MSDN and Technet libraries on the Microsoft website, use Google to look for pages and sit down and use it in depth before putting any requests for such changes to your employer.
John