I have a Perl program that takes a long time to run.  How can I check up on its progress - I want to know if it has got into an infinite loop or not, or if it's still running just how much longer it's likely to take  

Big question this one - lots of possible answers and options.  

For starters, if your program has a big loop that occupies most of the time you might like to put a printf statement in there, output to STDERR rather that STDOUT, and give the loop count, percentage of the way through, or something like that.   Here's a code sample:
Code:

select STDERR; $| = 1; select STDOUT; $top = 15; foreach (1..$top) {        $now = sprintf ("%3d%% through",$_*100/$top);        print  STDERR "\r$now";        sleep 1;        } print  STDERR "\n";

Few things to note:
* $| turns on autoflush mode (so that your carefully added alerts don't just get buffered).  
* \r is used rather that \n to ensure that each alerts overrights the previous
* printf is used to ensure all lines are the same length

If you have a loop that goes round "millions" of times, you won't want to print in every loop - follow your print statement with
           if (++$freq%50 == 0)
or something like that - it will print just one line in every 50!

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