Dr. House is some of the best unintentional autistic representation I have seen in popular media
I think the title is a slight overstatement, but I honestly feel this way. I'm not finished with House MD by ANY means so do keep that in mind, but I'm almost finished with season 2 so this is based off what I have seen.
Also: I am aware that there is an episode where they discuss the possibility that House has Asperger's. Obviously that term has fallen out of favor because Asperger was, you know, a Nahtzee, but I am going to emphasize that House has particularly low-support needs. My source is that I'm autistic and this is a topic I'm relatively familiar with. (Also. please take this with a grain of salt because David Shore also created "The Good Doctor" which is a comparatively pretty poor representation of autism, but I'm going to talk about House MD in its own vacuum.)
Lack of knowledge or concern for social cues. I don't really think this needs explaining, but House doesn't seem to have much regard or respect for social norms. He doesn't care much for social approval or maintaining relationships. I don't necessarily characterize this as specifically being an autistic trait, because this can greatly vary, but this is something I see in myself and other autistic people.
Strong sense of justice and morals. I see a lot of people calling House a "sociopath" simply because he isn't particularly empathetic. But the word sociopath gets thrown around a lot and it really doesn't characterize him well at all. I would argue that House feels cognitive empathy rather than the more emotional sense of empathy that most people experience, but equating empathy and morality is a big no-go. House has little concern for some ethical principles, as the show points out pretty often, but House is never looking to hurt anybody. House is always pretty dry and easily annoyed, but the only time we see him openly angry and upset is when someone endangers a patient. When Chase fucks up the angiogram, potentially putting a woman's life in danger, he holds it against him for ages. And in "The Mistake," when a woman dies and it has to be determined whose fault it was, House yells at Chase in the middle of the lobby over his negligence. Also, House does actually have empathy when it's necessary. He typically softens himself around younger patients and will make an effort to be calm, and when Stacy admits that she and Mark have been fighting and becomes upset, he tries to help her calm down and doesn't try to make the situation about himself. When he thinks that his "nemesis" from school is faking the results of his migraine medicine, he goes out of his way to prove that he's right - partially because, yeah, he wants to be right and get Weber back - but also because he sees this as cheating, and knows it's ultimately harming people.
Very few, specific interests. House doesn't seem to have a lot that he's interested in. His job is one of them, because he gets joy and satisfaction out of solving medical problems. It's also established that he's deeply invested in General Hospital and monster trucks (although I wasn't sure if that was a House thing or a Wilson thing? But he seemed pretty excited about it too). Other than that, he doesn't have many obvious or noteworthy things he's interested in.
Difficulty maintaining interpersonal relationships. Wilson is House's only friend, and House seems to be (mostly) content with that. He cares about other people, in his own strange way, but he consistently struggles to create and maintain personal relationships, whether because of his disregard for social niceties or because of his fear of vulnerability. Again, this may not necessarily be in relation to autism, but it's worth noting.
Odd speech patterns. I'm sick of media making it seem like all autistic people can't comprehend sarcasm. It is common for autistic people to take things literally, but autistic people also sometimes use sarcasm and metaphors more than the average person in verbal communication. I do this all the time. House is constantly saying weird, offbeat things, or making strange, vague metaphors, especially when he's deep in thought.
Stimming. Throwing his ball at the wall. Pacing. Spinning his cane around. Tapping his cane on the floor. Spinning it like a baton when he's alone in the room and trying to think. Sometimes he also nods his head back and forth when he's thinking.
Routine. This one is a little hard to spot, because House actually does seem to thrive when things are changing or new things happen. I see this mostly in House wearing the same things all the time. He's usually wearing some button-up and a blazer/jacket over it, and typically jeans and the same pair of shoes. The shoes are most likely for his comfort, but sometimes autistic people like to wear the same things a lot because it's what's most comfortable or they don't have to worry about unpredictability. Also, it seems like he eats the same thing a lot, since everyone knows he gets a dry Reuben sandwich.
This is just what I noticed and based on my personal experiences as an autistic person. This doesn't mean I think the show discusses autism in the most graceful or meaningful way - I just really like to break down my favorite characters and analyze them.