A front wheel with a quick release mechanism can be installed in two orientations: the lever on the left, or the lever on the right. Does it matter in which orientation it's installed? If so, would any problems result from installing it the wrong way?
In my experience, a front rim is symmetrical, and it doesn't matter which direction it's in. Unlike the rear wheel, where there's a drivetrain side and a non-drivetrain side, the only place where the quick-release handle can be. However, there are some other considerations to keep in mind:
Tires will sometimes have a tread direction. This is usually marked on the tread itself, in the form of an arrow with "direction of rotation" indicated. If you put a rim on a backwards from how you installed the tire, that could be swapped by mistake.
In addition, it makes sense to have the quick releases for both wheels on the same side. I make sure when putting a tire on the rim to set it up so, if both release handles are on the same side, the front tire is in the direction of rotation.
Disc brakes may introduce other considerations; other answers on this page address this. Outside of that, it mechanically makes no difference what side the quick-release is on.
Generally the QR lever on the rear tire is on the left, so as to not interfere with the derailer. It makes (a little) sense to put the QR lever of the front tire on the same side (at least if you have any OCD tendencies). But it basically doesn't matter, so long as the tire has no preferred rotation direction (and you don't have something like disk brakes that demands a certain orientation).
(And if the tire direction is wrong you can always remove the skewer and insert it from the other side -- the axle itself is perfectly symmetrical.)
Actually, there can be difference, if you are using disc brakes. For practical reasons, you should put the release on opposite side to the brake rotor to avoid accidentaly touching it. First, it may be still hot from braking, when you need to swap the tire, second, your hands can have oil (or your body oil mixed with sweat) on them and that can be bad for the rotor surface and brake pads.
On the road bikes it is considered to be a tradition to put them on the left, non drive side (front and back).
If I understand the question, I am pretty sure that bicycle tires are heteroflexible, and their orientation, which side, same side, opposite side, does not really matter.
However, I have been told it's best to mount them so that the lever itself points to the back of the bicycle, so it does not get trapped in anything and pop open.
I think that it is really important for the logo on the front hub to be the right way up when looking at the bike from the front.
The q-r lever should be on the left because it then does not have any possibility to entangle with the q-r lever of the bike in front.
The lever should also be folder to point upwards in parallel with the fork blade.
The tyre should be pointing in the direction marked forward on the sidewall.
Having one of these points wrong distresses me deeply. Particularly if the tyre has to be taken off and turned around so it aligns with the logo on the hub.
I have read on a Shimano disc-brake manual that you should leave the skewer to the opposite side of the disc.
That is so because, THEORETICALLY, some skewer levers could be turned beyond their closed position (parallel to the fork blade), and its tip could block the disk, causing a fall.
Practically speaking, I have never seen any skewer, be it in my bike or others', in such a position. Besides, since Shimano skewer is assymmetrical, it is much harder to get a good position if you mount it on the side opposite to the disc.
As of skewer orientation, I prefer closing it "upwards", so the closed lever is parallel to the fork blade, pointing up, with just enough room to wrap the fingers around it, and never too tight.
I was just told by my LBS that both my front tire AND wheel we're on backwards. My tire (Vredestein Triforzza) has a slight diagonal sipe (but no arrow on the sidewall). My wheel's decal was upside down. I said "OK, but the wheel is symmetrical so what difference does it make?". The mechanic said the cones in the hub are designed to rotate in one direction and may loosen over time if the wheel is installed backwards. I was experiencing speed wobble. I hope this fixes it.