I did a lot of swimming in NW Ontario when I was a kid, and I've spent more time swimming in lakes and rivers than I have in swimming pools. I find the phrasing of this question curious, because I've never heard any one use the words "wild swimming" nor have I ever considered swimming in a mountain lake or a river "wild".
None the less, there are some serious considerations when it comes to swimming outside when not swimming at a public beach with a lifeguard:
Factors to consider when swimming in lakes:
- Size & Depth
Size and Depth
Small lakes with beaches are the best to play in, they're calm, warm, and very tame. You can pretty much treat such lakes as swimming pools.
Larger lakes are where you need to be careful. Bigger lakes are deeper, have bigger wave potential, and can experience more severe weather. When swimming in a big lake, you can stay close to the shore, or choose to wander out into the middle/try to cross the lake. The difference is you can't just get out of the pool if you get tired, get a cramp, or inhale a mouthful of water. If you're out in the middle of a lake, no one is going to come to your rescue, so it would be good for you to learn how do preform a survival float, or drown proofing.
Hypothermia is a real danger when swimming outdoors. Lots of lake swimmers such as triathletes swim in special wetsuits that have great mobility for swimming. Depending on where you are you can find lots of lakes that are warm enough to swim in for long periods of time without getting too cold, and what the temperature is outside with the sun will have an effect on the water as well, but being in the water long enough, especially while moving through the water will slowly cool your core. If you start to get hypothermia in a large open lake, then you're in trouble if you can't get back to shore quick.
There is also cold shock, if you've never experienced swimming in icy waters, cold shock can be a killer, I've seen lots of kids dive into cold water for the first time where I'm from and come up choked for air, frantically flailing their arms, and stumbling to get back out of the water. If you're not prepared for it, and don't have experience with it, cold shock can shut your respiratory system down and really make you panic.
How remote a lake is obviously affects how quickly you can get help if something goes wrong, but less remote lakes have their own hazards. Unless you're at a public beach that's roped off and has a lifeguard, then your number one concern is often other people, particularly yahoos in speedboats blasting their music, drinking their beers and all looking out the back of the boat at their buddies riding their wakeboards, not paying attention to whomever might be swimming in the water in front of them. Be cautious on lakes where motorboats are present.
Heard of drift wood? Well it comes from somewhere, and floating wood in still water is trouble depending on how big it is. Dead heads are trees that have mostly saturated with water and float vertically just below the waters surface. Aside from devestating the hulls and motors of small boats, they can also give you a wicked bonk on the head if you're moving along through the water and make cranial contact with one, so keep your eyes out for what's in front of you, don't just get into your stride and watch the bottom, I have video of swimmers not watching where they're going and head-butting the side of my canoe. You can't even shout at them to warn them of obstacles, because they can't hear you under water. Be alert and aware of your surroundings when you're in the water.
Rivers are far more dangerous to swim in than lakes for obvious reasons. Depending on the size and speed of the water, rivers can generate very powerful currents that can sweep you away, suck you under, bash you against rocks, pin you into a log jam, or throw you off a waterfall. It's important to know what hazards are present in a river before diving in and going for a swim. You also need to learn how to swim in a current. Getting back to shore isn't as simple as aiming for shore and paddling, because you are going to be moving with the current. You have to aim for a location downstream then swim perpendicular to the water's flow in order to reach the side, and try to time yourself so you reach the shore the sametime you're flowing past the point you're aiming for. If you miss your mark, don't try to swim back upstream to get to it, keep swimming perpendicular to the current until you can touch bottom. Swimming against the current is pointless and wears you out fast.
Large slow rivers also often have commercial and recreational traffic on them, so once again you need to watch out for boats, as well as weirs (drowning machines) dams, and flood gates.
. . . . .
I often go out with "accomplished swimmers" into lakes and rivers, and they scoff at me when I hand them a lifejacket for a float downstream or playing on windsurfers. It's easy to change their mind about wearing a lifejacket simply by asking them, "How well do you swim while unconscious?" In rapid rivers especially, it's sometimes wise to wear a life jacket for the off chance you take a hit to the head by log floating by, or you roll over a rock and get slammed to the bottom. Or an overhanging log clips you in the head while you float by. They also provide extra warmth, padding (for bouncing off rocks when going for a swim in an extra "wild" river) and they can help you if you get a cramp while out over deep water. I know it's a pride thing for swimmers, but this is "wild water" so maybe consider it for your first couple times out if you're swimming out somewhere exposed or remote.