Kurt Russell sustained a broken ankle during the first week of filming, and got a week off. When he came back, all of the scenes where he was laying down were filmed. They followed that with the sitting-down scenes, then the standing-still scenes. Finally, the action scenes were shot. The last scene filmed was the "running" scene between Todd and Caine 607 near the beginning of the movie.
Writer David Webb Peoples has said that Soldier is a "side-quel" to Blade Runner (which he also wrote) because it takes place in the same universe and in fact the vehicles used by the Blade Runners - spinners - are also used in Soldier.
The trailer featured a spectacular space battle involving 20-30 ships around a planet. The film contained no such scene, nor could it plausibly have done so except perhaps as a flashback. It was probably a marketing ploy.
While listing the weapons Todd is trained on, you can he is capable of using the "Illudium PU36 ES,M" otherwise known as the Illudium PU36 Explosive Space Modulator. This is the same weapon Marvin the Martian is always threatening to use on Earth in his Bugs Bunny cartoons.
According to Paul W.S. Anderson, Kurt Russell worked out three or four hours a day for eighteen months to get himself into the "pumped-up" condition we see in this film. Anderson says the making of ;Soldier; was actually postponed to allow Russell to do this, because Russell thought it was so important to Sgt. Todd's character; Anderson made Event Horizon in the interim, and Russell made no other movies during that time.
Freeze frame the 'Trinity Moons' data readout display in the closing scene and you will find several references to "The Hitch Hikers Guide to the Galaxy". The 'Top Archive Specifications' comes up with ZZ9.Plurl.ZA (the sector in which Earth is reported to be) which comes up in Zaphod mode. On the right under 'Search Results' you can see 'Slartibartfast' complete with an 'HHG' reference number.
The snakes used in the film are Thai vipers and are extremely venomous. Stitches can be seen around their mouths to render them safe. Nevertheless when Kurt Russell is seen to be holding one of the snakes, it's not really his hand. The snakes were deemed to be too dangerous to be held by the film's star.