This is kind of an obvious one but it's easy to overlook. Say you're making a film and you've got a fairly low budget (or no budget) you're going to have to make a few sacrifices. With regard to set design, does it really matter if you've got a ceiling if the camera can't see it? Do your actors even need trousers if they're shown from the waist up? Okay, that's taking it to the extreme but you get the point. It's not just low budget productions though. A while back, I read about the costume design for period dramas. Very often, the designers would make parts of the costume as a one piece item. For example, the shirt part of a character's costume, underneath their jacket, might only be the part that can be seen. The reason is simple. With the same amount of material it takes to make a full shirt, you could probably make 3 or 4 other "fake" shirts which saves money. Obviously, this only matters on a large scale where you have many actors/extras who require costumes. Chances are, if you're producing a low budget movie, you wouldn't hire a costume designer. You'd just buy the required clothing items since it would be more practical than getting someone else to design/make them.
For my upcoming Vietnam War movie, I need to save as much money as possible. I simply can't afford full costumes for every single character so chances are, some costume items will be shared. I want every helmet to be a genuine Vietnam War era US Army helmet but I'll probably only buy four. However, if ten characters require a helmet, there won't be enough. The solution? Share the helmets and only give them to characters who appear in the current shot. The same strategy can be used for prop guns as well. Supplying ten characters with M16 rifles would cost me in the region of £3000. This is money that could be spent on others things so I'm better off having two M16s and sharing them between the characters in different shots. Storyboarding and previsualisation can be utilised to plan what needs to appear on camera for each shot.
Furthermore, do you really need genuine and authentic props/costume? Does the US Army helmet need to be a genuine 1960s era one? A genuine one would cost you upwards of £100 but for the same price, you can make two replica ones. A few years ago, I bought an Austrian issue M1 Helmet, replica cover and modern scrim band which ended up costing me less than £50. I intend to do this for the remaining three helmets that I require which means it will only cost me £200 instead of £400. Spend a lot of time on planning and pre-production and you'll save money.