Try this:

#!perl -w

# Uses
use strict;
use Win32::OLE;
use Win32::OLE::Const;
# Create MSWord object and load constants
my $MSWord = Win32::OLE->new('Word.Application', 'Quit') or 
die "Could not load MS Word\n";
my $wd=Win32::OLE::Const->Load($MSWord);

# Words and language to search for
my @words= ("quick","xxx");
my $language=$wd->{wdEnglishUS};

Win32::OLE->Option(Warn => 0); # Ignore OLE Errors
# Get synonyms from MSWord
for my $word (@words)
{
    my $synonyms=$MSWord->SynonymInfo({Word => $word, LanguageID => $l
+anguage});
    my $OLEerror = Win32::OLE->LastError();
    unless ($OLEerror)
    {
        if ($synonyms->Found)
        {
            foreach (@{ $synonyms->SynonymList(1) }) { print "$word: $
+_.\n" };
        }
        else
        {
            print "$word: Do not have any synonyms.\n";
        }
    }
    else
    {
        print "OLE Error: $OLEerror\n";
    }
}
Win32::OLE->Option(Warn => 1); # Reset to default OLE Error Handling
[download]

This calls the Found method on the synonyms object before trying to access the SynonymList.

Update: Modified program to handle missing thesaurus. After seeing Discipulus' post I tried the Italian thesaurus which caused the program to fail because I don't have the Italian thesaurus DLL installed.

Basically you're ignoring the error from OLE (Win32::OLE->Option(Warn => 0)) and checking for it yourself with Win32::OLE->LastError().

Note that the last line resets things so you'll get any subsequent OLE errors.

Update: Added comments to highlight <c>Win32::OLE->Option<c/> use. Changed last line to reset to default setting for OLE Errors.

Now attempting to move on. :)