For some reason when I tried to rendezvous two ships the blue maneuver node thing on my navball kept moving around. Apparently Mechjeb kept trying to chase it around the navball before doing the burn and completely missed the node.

I find this is usually caused by the SAS and or RCS ports are not near the COM. or that it simply doesn't have enough attitude control to be as precise as it need to be. the simplyest way to solve this problem without having to rebuild anything is to reduce the thrust of the engines (tweak while in flight when needed seems the best way) then it gives MJ enough control over time to get the burn more accurate.
also if its very close to finishing clicking the green tick is an option

The Maneuver node moves when the dV required to execute the node is getting low. Under 0.1 dV (by default) MJ stops chassing the node, but for some big ship it's still too much.
You can edit that value in the Maneuver Planner window (the tolerance setting in the lower right)