Be the perl interpreter for a second, and run though the for loop in your mind:

1. OK, so @alltypes is (".gif", ".jpg", ".jpeg", ".jpe", ".jfif")
2. For each element, print an error unless the string matches the extension.
3. So it doen't print for ".gif", but then it continues on to check if it ends in ".jpg" and falls over!

So what you're looking at is an and instead of an or. The simple fix in this case is to make use of grep:

unless (grep {$ext eq $_} @alltypes) {
  error("Your image needs to be a GIF of JPEG file!");
}
[download]

..thus, if the grep returns a false value, (the empty list) it means that none of the matches worked, so we need to print an error.

As a side note, proper indenting will make it easier for yourself and others to see what's going on at a glance.

Update: See rob_au's answer for how not to reinvent the wheel.

perl -pe '"I lo*`+$^X$\"$]!$/"=~m%(.*)%s;$_=$1;y^`+*^e v^#$&V"+@( NO CARRIER'