The biggest one would be growth. If you build your house between two branches, then in some period of time, your house could easily be in two pieces. Or if you anchored it to one branch, it could be simply swallowed up by the tree's growth, depending on how the house is attached.
Sunlight actually I don't think would be too much of a problem, unless the tree is extremely dense (coniferous trees, for example, might make it perpetual night). But with most other trees there's enough space for light to move around between the branches that you should be ok. It might lead to a sort of value system, where houses on the outsides of the tree, which have an actual view of the sun, are worth more than those which are on the inside and only get light that's been bounced around of few times first. People might try to build farther and farther up the tree, and farther and farther out on limbs, to make more expensive houses, but those houses would be quite unstable in any kind of wind, and the branches at either of those places are by definition much less strong than those near the trunk of the tree.
Leaf collection would indeed be a big problem, but the nature of the problem would change depending on whether this is a huge normal tree (leaves are normal size, the tree's just really old) vs. if its simply a huge version of a tree (and the leaves are scaled up to match). In the first case, you might be able to simply build a roof over every area, sloped enough to make the leaves slide off, but for the second a single leaf might be able to crush something, and you probably wouldn't want to live in a tree which shed leaves. Maybe an old dead tree would work.
Fire, obviously, would not be something you want to break out in this city. Small ones can be controlled, and even a house fire might not be able to break through the tree's bark before it went out, but some magic systems include the ability to make fires which can't be put out - and those would make short work of your tree.
Wind storms could be problematic for people and structures built on flexible areas of the tree.
The more things get built on a branch, the more it sags, and the more it bends the structures already built on that limb.
A slight misstep while walking would hurt (eventually, depending on the height of the tree).
Children's games most often require a large open space to run and throw things, and its one thing when your baseball falls in the neighbor's lawn, but a completely different story if the ball falls a couple hundred feet down out of your tree. A large pavilion could theoretically be built to give them an area to play though.
If any of the houses are actually cut into the tree, then you run the risk of eventually hurting/killing the tree if you go deep enough. Also again, if the tree doesn't die, then it's gonna keep growing and your house is going to change shape.
Traffic (even foot traffic) would require a huge 3D spiderweb of roads bridges and stairs in order to facilitate movement between branches, and that would probably greatly increase the difficulty of people unfamiliar with that section of the tree to navigate around, find a friend, or catch a criminal on the run. I'd suggest the mages look into levitation.
Also if it snows there, then you'd have to coordinate the shoveling of each person's house, so the guy at the bottom doesn't end up getting all the snow of the 25 houses above him dumped onto his roof.