Duo 2.5 Foreline Pump is slowly leaking oil

The primary wear/leak point in any oil bath vane pump is the motor shaft to oil reservoir seal.  The second one is the drain plug O ring. Over time, the shaft seal will leak. A small amount is normal and honestly of no concern.  You don't even need to vent to add oil, just unscrew the fill cap, add to the top line on the sight glass without overfilling, and screw the cap back on.

Overheating the pump will cause premature failure, so it's critical to make sure that there is sufficient airflow around the rough pump. Never install one in a closed cabinet except for the approved fan cooled quiet cover.   The fan on the end of the motor blowing over the oil bath is the cooling system, so filling the oil reservoir up to the top mark is best for the pump.

The blue mist filter is a separate part and typically installed on all Pfeiffer Duo oil pumps used on Agilent GCMS systems. it is not provided along with the pump from Pfeiffer nor Agilent. The blue mist filter is included in each paid PM service unless not used by the laboratory already.   It must be removed if the MS is run using Chemical Ionization or has been replaced with a barbed fitting and an exhaust hose to vent to your laboratory's exhaust system.    It is always better to have the rough pump exhaust plumbed to an exhaust vent system rather than to breathe the pump oil vapor and sample residue that comes out. 

How old was the previous pump?  These typically last years, then start slowly leaking for more years, then eventually leak enough to need oil added and the drip tray cleaned every week or two.  If this happens to anyone - let the Field Service Engineer know before the next Preventive Maintenance and they can be prepared in case the pump needs to be replaced and rebuilt.

(+) Rough Pumps on Agilent 5977x GCMS systems May 2021 - Files - GC/MS - Agilent Community

The previous pump was a rebuilt one that was about 2 years old. It was a sudden failure in some sort of gasket and all the oil leaked in the pan and the MS shut down.

It's there a safety risk in topping off oil while the pump is running?

The previous pump was a rebuilt one that was about 2 years old. It was a sudden failure in some sort of gasket and all the oil leaked in the pan and the MS shut down.

It's there a safety risk in topping off oil while the pump is running?

No, there is no risk adding oil while the pump is running.