What sort on checks do you need to perform to ensure that someone has not altered the contents of your html form and then submitting the altered form to the destinated perl script on your server?

Short answer: it depends.

First I'm not sure if you are asking about the structure of the form itself, or that data within that form. If you are talking about the data itself then you are going to have to do some data validation work.

Develop an idea of what your data should look like and develop code to validate it.

Unfortunately without more information about what your exposure and risks are I can't give you a better answer.