Honestly, this question isn't specific to dachshunds, but the person asked about it in relation to them so I'm including it in this themed week. The answer can apply to anyone considering a new dog.
There are many things that can be wrong with a new puppy. Some abnormalities are very obvious, but others aren't easily detected. Most people don't look closely at the mouth and teeth to see if there is an over- or underbite that could cause problems later. If you don't have a stethoscope and don't know what to listen for you might miss a heart murmur. Last week I saw a dog whose left ear canal never fully developed. Some health concerns are more serious than others, but all should be discussed.
That's why I recommend having a vet examine your pet prior to purchasing/adopting it, or shortly afterwards. Many breeders and shelters have policies that allow you to take the pet to a vet within a short period of time (2-3 days) and return it if there are any serious problems. Pets get into your heart quickly so it may not be easy to give that dog back if a problem is noted, but it helps to at least know what you might be getting into. There's nothing specific to dachshunds that would make it more important to have them looked at as puppies compared to other breeds. But it's always a good idea.