Yup, it's a definite no-no.
Among the many problems, the most common is a dislocated elbow (often called nursemaid's elbow) that can happen whenever you pull or hold a kid by the hands/wrists rather than picking them up under their armpits.
The thing that most folks (like me!) don't know until they take their kid to the ER and see the x-rays is their joints until about age 5 are almost entirely soft cartilege. When we saw x-rays of my then 2-year-old daughter's wrist and elbow after her first dislocation, it was really bizarre because there were all these empty spaces where adults have bones.
Once you get the first dislocation (and I assume the shoulder is the same way but I know you can get the elbow dislocated from doing what your husband does), subsequent ones happen more easily and frequently until the joint fully hardens into bone around age 5.
I'm not a doctor, but my daughter's right elbow has been dislocated three times so far, including twice within a month at preschool. In each case, someone had her by the hand and she resisted and tried to pull away. It's a fairly easy fix for the dislocation, but it's VERY painful to the child.
I have a niece whose elbow was dislocated doing exactly what your husband does by her grandparents, and a cousin whose kid had her elbow dislocated repeatedly by a grandparent who insisted it wasn't dangerous.
It's true that your daughter would/will let you know when she is injured, but the fact that so many kids end up in the ER every day from injuries caused by people pulling kids up by their hands should be enough for your husband to quit it.
http://www.emedicinehealth.com/nursemaid_elbow/article_em... has more details about it. Point your husband to page 2 at the above link where it specifically says that what he's doing causes this injury.
Hope that helps!