Captain reported numerous EICAS messages and controllability issues from rotation through to landing roll with a thrust reverser malfunctioning on deployment. The aircraft was turned over to maintenance for action.

Narrative

Just before rotation multiple amber EICAS (engine indicating and crew alerting system) messages appeared and disappeared shortly after lift-off. The first two messages were 'probe heat' and 'TAT.' I was unable to read the other messages before they disappeared. During the flight; while doing a cruise climbs the 'L TURB OH DET 1' status message appeared and then went away. During cruise with the left or center autopilot engaged; there was an occasional forward and aft jerking motion that could be seen on the yoke and felt. This motion was accompanied by the FO's (first officer) panel flood light flickering. With the Right autopilot engaged the jerking motion stopped; but the panel flood continued to flicker intermittently as before. Due to the numerous anomalies in addition to the left transponder and nitrogen generating system also being deferred; I contacted Dispatch and asked the Dispatcher to check with Maintenance Control for input. The response was nothing could be done until on the ground and a mechanic would meet the plane.The initial landing was smooth; straight and on center line. With the mains on the ground; I initiated reverse thrust by lifting the reverses to towards the idle reverse position. The aircraft yawed left and the right wing lifted up. I corrected for the yaw and brought the plane back to center line. As this was happening; the left reverser 'REV' was green and the right reverser was amber. As the airplane settled and after the nose gear was lowered; I was still unable to get the right engine into reverse. After a couple of seconds or so; the right reverser deployed. As I began to decelerate; I looked at the speed-brake lever and it was aft where it should be indicating they were deployed. I checked because the aircraft felt as though they did not deploy normally. After the right reverser deployed; I used reverse thrust and normal braking to slow the plane. After exiting the runway; the FO told me that in addition to the amber 'REV;' there were multiple EICAS messages that appeared and disappeared and that he did not have time to read what they were. After parking at the gate; I made the additional aircraft maintenance write-ups and talked to the mechanic that met the plane.