Other then the normal cleaning and oiling what other maintenance is critical to the proper function of my semi automatic shotgun, pistol or rifle?

Cleaning and Maintenance

The most overlooked maintenance is springs, and specifically the recoil spring. The recoil spring not only works the action of the firearm but, as the name implies, it controls the recoil force/impact of the moving action parts. Just like the shock absorbers on your pickup or car reduce the wear and tear on your the running gear of your vehicle, the recoil spring softens the jar between those parts and frame of the firearm. Just like the shock absorbers on your vehicle wear out and get soft so does the recoil spring. Regardless if it is a semi-automatic shotgun, pistol or rifle the recoil spring should be changed out as regular maintenance. It is the most prevalent cause of locking block and locking lug failure and frame damage.
As a general guide line we suggest changing the recoil spring:
Shotguns, using predominantly target load ammunition: every 8,000 to 10,000 rounds maximum. Shotguns using heavy field and magnum loads: every 2,000 to 3,000 rounds maximum.
Pistols: Standard service load ammunition, every 5,000 to 6,000 rounds maximum; heavy load ammunition (+P), every 2,000 to 3,000 rounds maximum.
Hammer springs set with use, age, and increase lock time. Firing pin return springs will eventually break.

Hammer struts on the 390/391 series of shotguns should be replaced every 20,000 rounds. 
At the same time inspect and replace the recoil absorber insert locate in the rear of the AL391 Urika/Teknys receiver, part index #120 http://www.brownells.com/.aspx/sid=57071/pid=29148/Product/C70564_ABSORBER__RECOIL__391__12GA would be in order.
Servicing of the of the AL391 Urika and Teknys family of shotguns is a regular requirement..
Service and repair parts for all Beretta current production firearms may be purchased from our parts distributor Brownells, Inc.
Availability of Service and repair parts for vintage and discontinued Beretta, Sako, and Tikka firearms is limited and many parts for older firearms are no longer available. Available parts may be purchased through MidWest Gunworks .
If the replacement or fitting of a part is not obvious to you enlist the services of a qualified gunsmith. Beretta Corporate policy does not allow this forum and or Beretta technicians to advise customers on subjects of a gunsmithing nature.