There are no serious cultural concerns about wearing inappropriate clothing in Vietnam. In religious buildings and government offices (or if attending a formal dinner), legs should be covered and sleeveless tops avoided.
Yes, Vietnam is in the tropics, but visit anywhere north of Hoi An between November and March and it can be cool, so pack some layers (a fleece or two). The rest of the year, and in the south, flip-flops or sandals, a T-shirt and shorts are likely to be your daily uniform.