The list of hot questions is shown on stackexchange.com and the MultiCollider (the dropdown in the top left). The idea behind it is, as far as I understand it, to present interesting questions across the whole network. I often find interesting posts that I wouldn't have seen otherwise when browsing the hot questions list, but I think that there is a lot of potential to improve the selection.
There are several aspect that could be improved in my opinion:
Questions can stay in the list for too long, making the list a bit too static for regular SE users. I've previously posted a feature request about this, and I still think that no question should be able to stay in the hot questions list for a whole week.
The current criteria are prone to select problematic questions. They value a high number of answers, which you find for example in list questions. So questions like this example from Math.SE have it easy to get into the list, while this type of question is regarded as problematic by most of the SE network and explicitly disallowed on many sites.
Being in the list of hot questions is self-perpetuating. Questions on the list get significantly more exposure, which means more votes, which then improves the position in the list of hot questions. The votes from outside users are also problematic as they represent mostly the popular appeal of the posts, not necessarily a judgement of the quality by an expert.
I've some ideas on what could be changed:
Exclude community wiki questions from the list. Those are usually big list-style questions that aren't a good example for high-quality content across the network.
Put less value on a high number of answers. The current method values (as far as I understand it) a high number of answers and a high total score of all answers. This preferentially puts more subjective or list-type questions to the top. A good question that got one high-quality answer that is highly upvoted shouldn't be at a disadvantage compared to a popular question that gets lots of opinions. Maybe counting only the first two or three answers and their combined score would be enough.
Weight external votes differently from internal votes. External votes from users that discover the question via the hot questions list shouldn't be counted in full, they mostly represent the additional exposure and the mass-appeal of the question, not necessarily the quality. But they also shouldn't be disregarded completely, a question that doesn't get any votes from the external users is probably too specialized to be of interest to a wide audience.
Normalize votes for each site. The voting behaviour varies a lot between different sites. Currently sites that have an above average number of votes are favoured compared to other sites. Normalizing the votes on a per-site base would put a stronger emphasis on the number of votes a specific questions gets compared to other questions on the same sites. It would prevent certain sites from being overrepresented due to their general voting behaviour.
These are just some rough ideas, I'm open to more suggestions.