Dress code is crucial at any such event since it is a sign that you really do care about the people organizing it and have shown respect towards the occasion. Not being adequately dressed because of it being just a rehearsal dinner is obviously a big mistake. On the wedding day, your dress should be formal and during the rehearsal dinner, nothing casual but nothing too formal should be chosen.
Unless there is a specific dress code mentioned for the rehearsal dinner, a semi-formal look should be taken on, but again, nothing too casual is befitting for the occasion either.
Dressing should go hand-in-hand with the venue of the rehearsal dinner. Again, if a dress code is not mentioned, than you can go ahead with whatever the venue asks for. If the rehearsal dinner is located at a home, a lighter stance can be taken in this regard. On the other hand, if the rehearsal dinner is set in a high class restaurant or by a catering service, taking on a more formal look should be opted for.
The food being served at the venue should also be another strong indication of what type of clothes you should wear at the rehearsal dinner.
Wedding Theme and Shoes
It is all about the wedding theme at the end. You would not want to be called to a Hawaiian wedding and be caught wearing a three piece suit, would you? Take the theme into consideration and when there are such formalities involved, it is most likely that a dress code will be set and mentioned to the attending guests.
Shoes are also important because being at a backyard rehearsal dinner would not be comfortable for women in high heels. Choose your shoes based on the venue as discussed before.