Is there a way to check to see if a link comes up with an error and if so then load an alternate link?

For example, say I have a link to a file on another server, if that link is down, can it then load the alternate link?

Why not. Add a field for alternate URL to DB or whatever else. Then regularly check the link via simple fopen() in a way like this:

PHP Code:

$fp = @fopen($link_url, "r");
if ($fp) {
   fclose($fp);
   $correctLink = 1;
}
else {
   $correctLink = 0;
}

if ($correctLink) {
   echo $usualLink;
}
else {
   echo $alternateLink;
} 


It is recommended that you run link checker once a day via crontab and store its current state somewhere instead of checking it on every script load.

Also please notice that this way is only acceptable if you have allow_url_fopen = On in your PHP config or in .htaccess for your site. Else you will have to implement this logic using sockets.