Kryten tells Rimmer that the Jump Remote must recharge and in the first Alternate Universe it does take a few minutes to recharge before he can jump again, but after that he jumps several times without any pause,
When Rimmer is in the other universe he walks down a corridor to find Lister but his right arm moves from by his side to across his chest as he turns the corner.
In the first Alternate Universe, Rimmer is still wearing a large H for "Hologram". The accident that killed him and the rest of the crew has not yet happened when he arrived so why would he be dead? Plus, as was established at in the first show, only one Hologram can exist at a time and it is based upon how vital they are to the ship. Rimmer as a Vending Machine Technician would be expendable.