A key procedure during takeoff roll is for all pilots (PF and PM) to monitor airspeed indication which provides a very good check of pitot functionality. Takeoff is to be aborted if airspeed indicators do not come alive as expected and compare favorably between multiple sources.
Static pressure sensor viability cannot easily be checked during takeoff roll. Once airborne, the altitude readout is the best way to detect an issue with static ports. Altimeter response should be consistent with climbout and track between redundant sources. I am not a pilot so I don't know how deliberate and intentional climbout procedures tend to be with respect to confirming reasonable behavior of altimeters, but that seems prudent to me. There have been a few accidents traced to tape having been left over static ports in order to protect them during ground procedures such that the static sensors were stuck at the reading for the departure airport. With this knowledge, I would certainly keep all altitude sources in my scan during climbout if I were assigned to Row 0.