No political system is perfect. However, I would say that there are two major weakness of a multi-party system.
First, there are too many choices. This might sound like a great idea in theory, but we need to remember that life is complex and complicated. It is hard enough to know all the issues with a few people in politics. If there are many more, then there will be lots of confusion and this could make the political system slow.
Second, with many parties, it is possible for a candidate to win with a non-majority of votes. If people are divided, for example, between 5 parties, then a person with 25% of the votes can actually win. This can be a dangerous situation and this person may not reflect the majority of people in the country. Something like happened when Hitler came to power.