Obviously re space combat while you could nominally see troop buildups etc, when an attack is launched you literally won't be able to 'see' them coming until they arrive

You've also then got a simple way of making terrifyingly potent projectiles, if, say, a ship returning to earth doesn't manage to slow down and punches straight through the planet. Or this could have consequences like a big taboo on pointing directly at anything in case something goes wrong

Depending on how the hyperdrive works it could be doing something like decoupling gravitational and inertial mass...which on a lower power setting could give you plausible anti-gravity hover vehicles, long term floating installations in the atmosphere etc

Relativity does a lot of weird shit close to light speed like time dilation, length contraction etc so could also potentially be used for like sending people or tanks through things that would usually kill them. Fun fact that's what happens with some high energy particles in earth's atmosphere