As a general suggestion from Support perspective, make sure you have an inventory with all your Check Point appliances (Mgmt + GWs) and try to have these details handy:
- Enabled SW blades ('enabled_blades' command)
- Custom hotfix level, if any special hotfixes (cpinfo -y all... this will come in handy when creating cases with support)
- Jumbo Hotfix level on each appliance ('installed_jumbo_take' for R77.30 / 'cpinfo -y all' for R80.10)
- IP address/mask
- MAC address (needed for RMA purposes)
- Service contract dates
You can also log into your UserCenter account and check any previous tickets that were created for any of those appliances, this may give you a good understanding of the general issues (if any) that previous admins have experienced.
Have a good backup policy (save configuration/backup/mds_backup/snapshot, anything... everything!!). Very important - Get the backups out of the appliance)
Make sure you have enough disk space on appliances (df -h), specially log/mgmt servers.... if you have SmartEvent, check here too.
If you want to go one step further, you can even run the health check script from sk121447 on each appliance... very easy to do, and it can get you a starting point to see your devices' current status.
Ultimately, make sure you have supported/upgraded versions everywhere... lots of enhancements and new code have been added to the latest releases:
sk106162 - R77.30 Jumbo Hotfixes
sk116380 - R80.10 Jumbo Hotfixes
As some people already mentioned, change passwords/users. I cannot stress this enough
You can also run something like "top" on each appliance just to get an idea of how much load it's handling, potentially identifying any device that's constantly at more than ~ 60-80% CPU usage during business hours (may need further review to understand why, or may even need to be replaced with a more powerful unit if it's handling too much load all the time)
Hope this helps!