After Rimmer rides off on his motorcycle after ordering the waxdroids to attack, in the wide shot of the waxdroids advancing from their position seconds later, he's still in the background where he was before.
When Rimmer is recounting his RISK campaigns, he mentions that he threw two dice on the attack. In RISK, the attacking team throws three dice rather than two (assuming he has at least three armies, and he does in this scenario).
In close up shots of the brick walls of Lister and Cat's jail cell, it's obvious that they are completely flat and brickwork is either wallpaper or has been painted on.
When Rimmer and Kryten arrive on the Waxworld planet, Chris Barrie's breath is visible due to the cold. As a hologram he shouldn't have breath, this is actually the reason he and Kryten have gone first (in case the atmosphere isn't breathable)
When Rimmer and the Cat leave the living quarters to meet Lister and Kryten in Starbug, the chair that Rimmer was sitting in spun after he quickly got up. Since Rimmer is a hologram the chair should not have moved.
No explanation is given to how Rimmer, who is a hologram, is able to ride a motorcycle, and not pass through it.