Clearly, the first thing that should go wrong is a mysterious death.
This could happen before the adventure starts (especially if it seems like the adventurers might be reluctant to partake in your little escapade), in the form of a noble-woman looking for her missing son. This could lead to some investigation wherein the characters discover that there is a nefarious plot by the operators of the menagerie (which is what everyone will expect) OR the menagerie operators could just be covering up an accident or a mistake, such as a heretofore unknown indigenous Farikan population that has not taken kindly to the encroachment onto their land and the slaying of their respected totem animals (the tigers).
Or (and?) some more mysterious deaths could take place once the characters join a hunting party and start crashing around in this exotic jungle. I am reminded of old jungle exploration movies where the members of the party (usually starting with the porters) start getting picked off one or two at a time, while struggling to travel through the dense jungle undergrowth... This would be attacks by the indigenous peoples, tigers (to whom porters are tasty treats) and other jungle inhabitants.
This could culminate in a big showdown with the indigenous folk (who may or may not have taken some folks prisoner), which may mean just beating them into submission, or they may have to succeed in some other sorts of challenges (they may have to best some appointed champions in a ritualized contest, rather than doing actual combat, whatever). Hopefully you can throw some sort of twist into this meeting, so that there seems to be a piece of the puzzle missing (for instance, these indigenous folk are not tiger-worshipers, as the party has come to suspect, and they are angry about something that the hunting party hasn't even done). This is to get the players on their toes for the second portion of the adventure, below.
Once the party has successfully dealt with the folks who have been killing / eating / kidnapping the members of the hunting parties, and they return to the fancy magical portal, that is when the arcane disaster should strike. A piece of the magical portal (without which they cannot journey home) has been taken, probably by the other (other? there are two unknown indigenous peoples?) indigenous peoples. And off the party goes, to wreak yet more havoc. To get their arcane doohickey back, the party will have to deal with this second group of people in some way...
Or... something else.