This probably counts as speculation but still
How physics seems to work in the ME universe
1. Conservation of energy. I was thinking about how in depth I should make this bit but I am rather sure that the law of conservation of energy is warped or destroyed in the ME universe. How? well consider two weights on, for want of a better description, a bicycle chain length (H), with one weight hanging on each and an a gear at the top which the chain runs over the gear leads to a generator. Give weight 1 a mass of (M) and weight 2 a mass of (M+D). Now place a mass reducing circuit with a switch under weight 2 and let the system move. Start with mass 2 at the top and the circuit off. Gain in GPE for the system would be G*D*H where G is acceleration due to gravity in wherever this is done. This can be made into electrical energy in the generator. When weight 2 reaches the bottom, it touches a button which turns on the mass reducing circuit making its mass become (M-D) and the system generates another G*D*H of energy. This is said to require current proportional to mass changed (2D), volume of effect (unknown since it depends on densities and sizes of the weights) and time (you could go to work out time in terms of M and H and G). The point of this becomes: by finding the right values for M, D, H, G, resistance of the circuit, volume of the effect and the coeffiecient for how much electrical current is needed to make the effect (by sheer omnipresence of its use I assume this coefficient is not very much). You could find a place where this system would be able to power itself and more perpetually.
2. Conservation of momentum. Whether or not momentum is conserved in ME is a bit more difficult to decide. In the codex for mass accelerators; the implication is that a projectile leaving a mass effect field will suddenly gain or lose momentum when it crosses the boundary (or there would be absolutely no point of usign mass effect fields in weapons since your highly accerelated bullet would lose most of its speed as soon as it leaves the barrel. the SMG recoil mod in ME3 also seems to imply that an object moving in a collapsing mass effect field will also gain or lose momentum (split second increase in mass of weapon during firing so the same recoil momentum is delivered as a low velocity high mass arrangement, but since it reduces recoil overall, evidently when the mass is reverted, speed it kept constant and hence momentum is lost). However the codex entry for FTL Drive does something to imply that momentum is conserved somewhat when it says: "If the field collapses while the ship is moving at faster-than-light speeds, the effects are catastrophic. The ship is snapped back to sublight velocity, the enormous excess energy shed in the form of lethal Cherenkov radiation" If at FTL speeds, a collapsing mass effect field had the same results as those used in weaponry then you would get an imaginary number for the mass of the ship (relativistic mass is rest mass over the square root of (1 - v^2/c^2) where v is velocity and c is speed of light) if v>c then relativistic mass is a real number over a complex number. But there is no reason why this should not be theoretically possible, complex numbers are used to solve many real world problems. Conclusion: someone got a bit iffy about complex numbers for ship masses, but otherwise conservation of momentum is ignored which could be used to make another series of perpetual motion devices. Also I would challenge the methods of creating propulsion listed in the codex as being wasteful when using this momentum creation, you could contain the entire propulsion system within a ship and not have to throw out anything as exhaust.
3. 'Supernova bomb' something I am surprised that the turians or Alliance didn't do, It sounds like the protheans did. Basically get a large Eezo core and direct it at a star. By reducing the star's mass you force it to blow off (very hot) mass since the pressure exerted from the inside outweighs the gravitational pull inwards. Or make it gain mass so it pulls in gasses and dust that used to just be orbiting it. This will make the star have a shorter lifespan, and If you can get a star heavy enough it will start to convert helium and in doing so, spread to several times its current size. lure reapers into a system with no planets worth keeping and warp the mass of the star to vaporise your opponents (and your own ships doing the mass warping). All about sacrificing few for many and that.
I may add to this as I think of stuff. I will also inquire as to whether diagrams would count as personal images so I could make some to help indicate points