Yes, there more than a few downsides to asking this question. First of all, how well does the person you are asking really have the ability to answer this question? If you are asking someone in HR this question, they may have little idea of what a legitimate answer is here. Even the manager may not know if the team is still relatively new and things aren't so well-known in terms of social dynamics and getting things done. The other side is how prepared are you for the linguistic gymnastics you may be starting with this question as there is more than a slight chance of any answer being so loaded with buzzwords or vague that it has little value unless you know how to follow-up with some harder hitting questions. For example if they claim that they co-operate and deliver well for a strength, are you prepared to interrogate that further?
On the flip side, I'd be more tempted to ask for a bit of team history:
- How long has this team been together?
- Who has how many years here?
- What roles do the various people tend to play usually?
That would be far more useful to my mind than the question that may be perceived as rather loaded to my mind. While I can admire the effort, I'd wonder how well would any company have studied the team dynamics to find their strengths and style to the point of being able to disclose them.
The comment about asking this to the person without knowing how well they answer gets into those "linguistic gymnastics" I mention above as I can easily foresee someone stating something akin to, "We hire only the best here," or something else that is boilerplate for an answer that would require some probing to discover the answer was just someone trying to be polite rather than offer an accurate answer. Another generic answer would be that "everyone gets along so well" that one could wonder if there are hidden hostilities or is the team really a bunch of mature people that do work well together.
Rather than ask for weakness, I'd restate the question to be, "What is your development team's greatest challenge?" so that it isn't taken to be someone intentionally trying to stir up trouble but rather trying to gain some insight into how the team is seen.