Welcome to the UK List of
TeX Frequently Asked Questions
on the Web

The errors

! You can't use `\spacefactor' in vertical mode.
\@->\spacefactor 
                 \@m 

or

! You can't use `\spacefactor' in math mode.
\@->\spacefactor 
                 \@m 

or simply

! Improper \spacefactor.
...

bite the LaTeX programmer who uses an internal command without taking “precautions”. An internal-style command such as \@foo has been defined or used in a private macro, and it is interpreted as \@, followed by the ‘text’ foo. (\@ is used, for real, to set up end-of-sentence space in some circumstances; it uses \spacefactor to do that.)

The problem is discussed in detail in “@ in macro names”, together with solutions.