With the standard objections in mind (see the other answers for those), let's see if we can't find some ways to beef up your super-soldiers.
Humans are actually pretty well optimized in a lot of ways, so this one isn't as straight-forward as you might think. There are some basic upgrades we can get away with that won't fall foul of the standard logistical and operational issues, but they won't necessarily qualify you as "super."
(For the purposes of this I'm going to be leaning heavily fiction. Not going to even try to justify these things in scientific terms.)
While electronics and gadgets are almost always going to be better than whatever meat upgrades you may be sporting, there are a few things that can make you far more effective without necessarily breaking you biologically.
First up, let's tweak the retinas to add a fourth cone type that is sensitive to mid-range infrared. The cone density can't change much so your color discrimination may be a little reduced, but being able to detect differences in temperature is useful enough.
Still in they eyes, a more effective structure of the iris to respond to light levels more rapidly and a nictitating membrane to protect against dust and such - well, it works for reptiles.
Next up, a bit of tinkering with the ear to increase the frequency range and sensitivity. Maybe optimize the ear itself to be a little better at directing sound waves so that our soldier has near-canine audio accuity. Let's add an actuator muscle to the Tragus while we're at it, so that your soldier has some way of reducing sound sensitivity at will.
I'd avoid modifying smell, taste or touch too much, except maybe to add some olfactory receptors for important chemical markers. We don't need a bomb dog, but being able to discriminate dangerous environments by smell seems useful.
Human muscles are strong enough, when fully utilized, to seriously damage themselves and the things they're attached to. You've all heard the stories about hysterical strength, women lifting cars off children and so on. The aftermath isn't pretty though: broken bones, ripped tendons, torn muscles. Nasty stuff. Electric shocks can do damage by causing muscles to spasm at levels much higher than you can normally sustain, ripping and tearing and breaking bones. Not fun.
Tendons - those little bits of collagen and elastin that connect muscles to bones - are pretty strong, but we could make them stronger. Lacing the tendons with other biological materials (lignins for instance) could significantly increase the connection strength, allowing higher muscle strength to be developed or utilized.
Similarly, skeletal muscles can be reinforced with stronger fibres to allow them to withstand greater stresses before tearing.
Strength comes at a cost however. The energy for every action comes from somewhere. That leads us to:
Your whole body runs on supply and demand. Every muscle twitch - from the beat of your heart to the thousands of tiny muscle movements that allow me to type this - takes energy. Mostly that's means carbs and oxygen, although fast-twitch muscles aren't always aerobic. Either way you'll need damned good lungs and a robust circulatory system.
For lungs you'll want to work out how to increase the gas exchange efficiency as best you can, and maybe give them a bit more internal surface area to maximize the available oxygen absorption.
Circulation is a bit more difficult. You can't screw with the blood much, other than increasing the red-cell count a little, nor can you just pump more of it around without breaking a whole bunch of things. You can change the layout of a few things without breaking the whole, make the heart a bit more robust and maybe add some additional filtration in the liver and kidneys. Be careful not to over-pressure the brain though.
As for the fuel itself... improved liver function and better lipolysis pathways would be good. Maybe figure out how to get more efficient catabolism to produce all that ATP your muscles need.
Stopping bleeding is a big thing in trauma response. The body does an OK job of it, but large injuries are prone to leaking a lot. Would be nice if we could increase redundancy in the circulatory system and add some involuntary sphincter muscles to restrict blood flow in damaged areas.
We can add some modified adipoctes that store sticky material that helps seal things closed, from broken blood vessels to torn skin. Scarring might be significantly worse, but it beats all hell out of bleeding out.
That's after you get damaged of course.
Since we're already weaving lignins into other parts of the body, let's repeat that through all your subcutaneous tissues. That makes you a little harder to cut, but at the cost of a loss in flexibility. Shouldn't interfere with heat dissipation too much, but may over-insulate the muscles themselves. Be careful with this one.
And while we're at it, wrap bones in the stuff too. Add some rigidity and impact dispersal to the periosteum, protecting from impact breaks and the like. This should also strengthen the bone somewhat without having to change the bone structure, so you're not adding a lot of weight or reducing the marrow volume.
I'm sure we can come up with more along this line. It's a little bit sciency without being in any way actually realistic, but that's part of the fun of SF.