Prone to major back problems, and temperament issues. In dog bite studies they have come out on top of the most aggressive dogs that bite the most (although it is true that being bit by other breeds might put you more at risk for serious injury). I would say this shows a problem in the general population regarding impulse control and bite inhibition, which are traits that do have a strong innate temperament component. MEaning, sure you can train, but you might have to put in a lot more effort just to get a dog that is even halfway trustworthy and mannerly (a lot of dachshunds I have seen are not really either). This is not to say they are all bad, but like many dog breeds that have been overbred due to popularity AND bred for major extremes in appearance, there are a lot of issues you should be on the lookout for or at least expecting. I would put a ton of research into finding a truly reputable/responsible breeder if you are going to buy. And by that I do not mean a show breeder who breeds for champions, but a breeder who you believe ACTUALLY cares and breeds with health and good temperament in mind, and then puts effort into properly socializing the pups prior to sale. Or I would rescue an older adolescent or even adult that you could see what their health and temperament were like.
This kind of comes across that I hate this breed or something, and that's not true. I even have a favorite dachshund. This dog likes me but hates all children and I would never ever let it near my kid or vice versa because I KNOW she would get bit. And her owners have literally spent over $10,000 on medical issues for the dog including two back surgeries.