If you just click on the submit button without entering values in mandatory field, some text or (*) would be displayed besides those edit fields.
So you can use text checkpoints accordingly to compare whether those fields are filled or left empty.
Yes..its better if we can check with the Functional spec's which are mandatory fields and test them.
For eg. if you have 3 fields and the error msg appears individually at the bottom of the txtbox, then u can submt the form without filling the values and then check the webelement's(error msg) exists or not.