Is there anything wrong with men wearing shorts (i.e. short pants)?
If there is, why would it be any different than wearing short sleeves?
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Piskei Teshuvos in the beginning of Siman 2 cites Igros Moshe and other Acharonim who delineate the guidelines of modesty as it applies to men. The points that emerge are:
1) Modest dressing for men is not an absolute obligation, but it is very significant (וצריך ליזהר etc.)
2) The definition of immodest in this respect is if you'd be embarrassed to be seen like that in your house by a casual guest.
3) Thus, there is room for leniency to wear short sleeves etc. due to the heat. [Whether this applies to shorts would probably depend on the person and the norms of his community. There are people who would not be caught dead wearing shorts; for them it is presumably a problem.]
4) Nevertheless, a Talmid Chacham should be stringent in these matters, taking care to "walk modestly before Hashem" as much as possible. Even though most people do not qualify as a Talmid Chacham nowadays, it is appropriate for anyone to increase his level of modesty.
Note: The halachos are more stringent with regard to davening. What is allowed in general may not be appropriate during prayer.
The Mishna Berura in 2:1 says that men should not uncover what is normally covered. In his time (or the time of those he is quoting), men did not uncover above their elbow and so he quotes this as an issue of "Tznius and Bushah before Hashem". This is not true today where many bnei Torah wear short sleeves. (Of course, there are people who walk outside shirtless or sleeveless, but society would not consider this "appropriate attire"- e.g: no shirt, no shoes, no service!) I don't know of any distinction in halacha for men between arms and legs except regarding the norms of society.
The mishna brura then quotes a gemara that says talmidei chachamim should wear clothes that do not show any part of their body.
So it would seem technically mutar, but not best practices. It is interesting to note, however, the difference in length between the shorts of, say, the 70's (very short) and those of today.
I seem to be echoing Dave's answer, just different references.
The Sefer BeYishak Yikare (Siman 2) writes "En Raui-not proper" to wear shorts (En Raui doesn't mean it's Asur but Lechatehila should be followed). However, it is not clear what the definition of shorts are. It's possible that below the knees would be fine.
Nothing wrong with it according to my humble opinion. But some Poskim might find some area of Tzniut that applies to this.