One of the interesting, if sometimes sad, issues with chess Olympiads is which teams actually make it to the tournament. Having served on the Technical Administration Panel (TAP) in 2010 and 2012, there is a lot of uncertainty about whether a team has made it to the host city, and a lot of late night ringing around occurs.
On at least two occasions I have seen half a team turn up (only 2 players in 2008 and 2012) and been allowed to play. The rules were actually changed after 2008 to require a minimum of 3 players present for a team to be valid, but in 2012 FIDE President Kirsan Ilyumzhinov just waved his hand to allow Burundi to compete (they went 0-11 and scored 3.5 game points).
One of the weird stories for this Olympiad involves the team from Pakistan. According to this report the Pakistan Sports Board has refused to allow the team to travel to Azerbaijan. The PSB currently does not recognise an official Pakistan Chess Federation, as there are at least 3 competing federations. Apparently they have requested the team not be allowed to leave the country, which sounds like pretty serious stuff.
Papua New Guinea went through a similar situation in the lead up to the 2014 FIDE General Assembly, with a former president claiming he was still running the federation, despite a new executive being formerly elected. While it did not effect the participation of the team, it did mean that it was unclear who the PNG delegate to the GA would be. In the end FIDE, after some deliberation, simply recognised the candidate who was going to vote for Kirsan Ilyumzhinov, which of course was the previous president. Oddly, part of the reasoning was the claim that a Federation needed to be recognised by the countries National Olympic Committee or Sports Ministry, a 'rule' they seem to be ignoring in this case.