You don't get many bad events, although I hate the event about riders harassing pilgrims to Mecca (lose prestige-legitimacy or a lot of gold).
The succession is so far harmless, aside from the fact that you have no control on the stats of your posible sultan. If you go for a Circassian ruler you get 15 army tradition, but with no Circassians provinces you can only use the -5% power cost for a year mechanic.
If you shose a sultan from another group you can use the sell slaves (to get gold) or rise aditional support for manpower, but at the cost of low legitimacy.
The low legitimacy can be a problem for some events... like one related to who will be in charge of protecting the route to the holy cities, but so far I have only see it once.
If you expand into an area with Circassians, well you can easily stack army tradition and also get the extra gold/manpower from the mamluk goverment interactions.
A big problem I found at the start is that the nobility state have to many provinces, one or two events and you can get the Aristocratic Coup disaster really early in the campaing, cripling your economy with -25% trade income and taxes.
You can avoid it by taking away the provinces, but doing so you will very likelly deplete your initial manpower of only 18k with noble rebels.
Aside from that not much. Ethiopia can be a nuisance at the start. The ottomans are always a menace and if you expand south, well you can have problems with some colonial powers like spain or portugal.
The Mamluk goverments is really cool, but so far we don't have a way to know the stats of the posible sultan, only his age and the legitimacy that he will have at he start (And so far I already got a really competent 0, 2, 0 with 100 legitimacy so a good ruler is not a warranty) and depending of your choice some of the unique interactions will have absolutely no efect.
They seem overpowered right now. But I think that being so close to the ottoman empire is always a hard start.