My advice is do not attempt renaming but first generate a list of moves and then review that list

See similar questions Changing filenames, Multiple File Rename

So, I would start with a program like

#!/usr/bin/perl --
use strict; use warnings;
use Data::Dump qw/ dd pp /;
use File::Basename qw/ fileparse /;
use File::Copy qw/ move /; # RENAME
Main( @ARGV );
exit( 0 );
sub Main {
    my @files = qw'
    err/error.txt
GridSquare_0000000077_FoilHole_0000000001_Data_0000000002_20120315_103
+721.jpg
GridSquare_0000000077_FoilHole_0000000001_Data_0000000002_20120315_103
+721.xml
blah_foo.jpg
blah_bar.xml
blah/foo.jpg
blah/bar.xml
    ';

    my @rename = makeRenameList( @files );
    fakeRename( @rename );
}

sub fakeRename {
    print "\n";
    for my $name ( @_ ){
        print "rename ", pp( $name ), "\n\n";
    }
}

sub makeRenameList {
    my @fromTo;
    my %rename_index  = (
        qw/ .jpg  1 .xml 1 /
    );

LOOP_FROMFILE:
    for my $fromFile ( @_ ){
        my($directory, $filename, $suffix) =  $fromFile =~ m{^(.*?)(?:
+([^/]*?)(\.[^\.]*))?$};

        if( not exists $rename_index{lc $suffix} ){
            warn "Unknown suffix ($suffix) ignoring($fromFile)";
            next LOOP_FROMFILE;
        }

        my $toFile = join '',
                        $directory,
                        $rename_index{lc $suffix}++,
                        $suffix;
        push @fromTo, [ $fromFile, $toFile ];
    }
    return @fromTo;
}
__END__
[download]

Which would print

Unknown suffix (.txt) ignoring(err/error.txt) at - line 41.

rename [
  "GridSquare_0000000077_FoilHole_0000000001_Data_0000000002_20120315_
+103721.jpg",
  "1.jpg",
]

rename [
  "GridSquare_0000000077_FoilHole_0000000001_Data_0000000002_20120315_
+103721.xml",
  "1.xml",
]

rename ["blah_foo.jpg", "2.jpg"]

rename ["blah_bar.xml", "2.xml"]

rename ["blah/foo.jpg", "blah/3.jpg"]

rename ["blah/bar.xml", "blah/3.xml"]
[download]

Next I might change sub makeRenameList to

        my $transform = "";
        $transform = \&transformJpg if  $suffix =~ /^\.(jpe|jpg|jpeg)/
+i ;
        $transform = \&transformXml if  $suffix =~ /^\.xml/i ;
        if( not $transform ){
            warn "Unknown suffix ($suffix) ignoring($fromFile)";
            next LOOP_FROMFILE;
        }
        
        my $toFile = $transform->(
            $fromFile,
            $directory,
            $filename,
            $suffix,
            $rename_index{lc $suffix}++
        );
        push @fromTo, [ $fromFile, $toFile ];
    }
    return @fromTo;
}
[download]

sub transformJpg {
    dd transformJpg => \@_ ;
    my( $path, $dir, $file, $suffix, $idx ) = @_;
    $file =~ s/^.(.*).$/$1/;
    return "$dir$idx$suffix";
    return $path;
}
sub transformXml {
    dd transformXml => \@_ ;
    my( $path, $dir, $file, $suffix, $idx ) = @_;
    return "$dir$idx$suffix";
    return $path;
}
[download]

and so on and so forth, until I'm satisfied with output of fakeRename, than I might call realRename :)