Is "if any problem, please call me" grammatical?
This omission of syntax in informal speech (and especially emails) is quite common and I would hesitate to call it ungrammatical. It is an example of ellipsis:
ellipsis |iˈlipsis| noun ( pl. -ses |-sēz|)
the omission from speech or writing of a word or words that are superfluous or able to be understood from contextual clues. [NOAD]
The point is, you did understand from the context of the sentence what the sender intended. Certainly you would not want to write that way in formal prose, but the criteria I would use to judge the usage here would be
- Is the meaning readily understood?
- Does the text need to convey good communication skills?
If you can answer yes to the first and no to the second, then you don't have to worry about using ellipsis in the communication.
Yes, you are correct. The first clause in the sentence is ungrammatical because it lacks a verb. It looks like laziness on the writer's part when they should have said if there is any problem, or if you have any problems.