Read the file line for line and use a flag to indicate whether you want to collect lines or not, you could also call it a simple state machine:

my $errormatching=0;
my @errortext='';
while (<>) {
  if (not $errormatching) {
    $errormatching=1 if m{^\s*'Errors' =>};
  }
  else {
    if (not m{^\s*\]}) {
       push @errortext, $_;
    }
    else {
      process_error(@errortext);
      @errortext=();
      $errormatching=0;
    }
  }
}
[download]

UPDATE: Fixed typo where I used [ instead of ] in the regex

Right, I wanted to suggest some state machine along this too:

#!/usr/bin/perl

use strict;
my @lines;

sub flush {
        return unless grep(/'Errors'/, @_);
        print "Got:\n\t", join ("\t", @_), "\n";
}

while (<>) {
        # trigger on last line of an error message
        flush(@lines,$_),@lines=(),next if m{^\s*\};\s*$}; 
        # triggger on next timestamp
        flush(@lines),   @lines=()      if m{^\s*\[\d\d\d\d\/};
        push(@lines, $_);
}
flush(@lines);
[download]

However, all solutions I have seen so far trigger evaluation with the next timestamp only. When using tail -f, the error will be processed only when the next log-line with a time-stamp is encountered - which might happen some hours or days later. IF seeing an error ASAP is important to the OP, the evaluation should be triggered additionally by matching for }; or by some timeout-mechanism, e.g. using alarm().
Update: final flush(...) added

You might have been mislead by a bug in my solution where I used the wrong bracket for end of error detection (which makes the script not work at all), but it does process the error when ] is encountered, i.e. well before the next log-line.

Use $/ to skip over the bits you aren't interested in:

#! perl -slw
use strict;

$/ = "'Errors'";
while( my $junk = <DATA> ) {
    local $/ = "\n[";
    my $errorData = <DATA>;
    last unless $errorData;
    chop $errorData;
    print "'Errors' $errorData";
}

__DATA__
[2008/10/14 10:57:18] [55] DEBUG Austin::API::vendor_api - Initialisin
+g the APIGalileo
[2008/10/14 10:57:18] [41] DEBUG Austin::Suppliers::Common::Location::
+init - Setting Up Generic Locations
[2008/10/14 11:15:22] [147] DEBUG Austin::Controller::default - $VAR1 
+= {
          'Errors' => [
                        {
                          'ID' => 'noRates',
                          'Error' => 'No Rates for given dates/times',
                          'object' => '/var/website/modules/Austin/CB/
+Search.pm',
                          'Location' => undef,
                          'line' => 371
                        },
                      ]
        };
[2008/10/14 10:57:18] [245] DEBUG Austin::XV::Trip::set_time_zone - Ch
+ecking timezone with agent UK
[2008/10/14 10:57:18] [247] DEBUG Austin::XV::Trip::set_time_zone - Se
+tting timezone to Europe/London
[2008/10/14 11:15:22]
[2008/10/14 11:15:22] [147] DEBUG Austin::Controller::default - $VAR1 
+= {
          'Errors' => [
                        {
                          'ID' => 'noRates',
                          'Error' => 'No Rates for given dates/times',
                          'object' => '/var/website/modules/Austin/CB/
+Search.pm',
                          'Location' => undef,
                          'line' => 371
                        },
                      ]
        };
[2008/10/14 11:15:22]
[download]

Outputs:

c:\test>junk1
'Errors'  => [
                        {
                          'ID' => 'noRates',
                          'Error' => 'No Rates for given dates/times',
                          'object' => '/var/website/modules/Austin/CB/
+Search.pm',
                          'Location' => undef,
                          'line' => 371
                        },
                      ]
        };

'Errors'  => [
                        {
                          'ID' => 'noRates',
                          'Error' => 'No Rates for given dates/times',
                          'object' => '/var/website/modules/Austin/CB/
+Search.pm',
                          'Location' => undef,
                          'line' => 371
                        },
                      ]
        };
[download]

#!/usr/bin/perl --

use strict;
use warnings;

my $line = "";
OUTER:
while (<DATA>) {
    if (/^\[/) { # could use \[\d{4}
        $line = $_;
    }
  INNER:
    my $i = 0;
    while (<DATA>) {
        if (/^\[/) {
            print $line, "\n" if $i;
            $line = $_;
            next OUTER;
        }
        $line .= $_;
        $i++;
    }
}

__DATA__
[2008/10/14 10:57:18] [55] DEBUG Austin::API::vendor_api - Initialisin
+g the API Galileo
[2008/10/14 10:57:18] [55] DEBUG Austin::API::vendor_api - Initialisin
+g the API Galileo
[2008/10/14 10:57:18] [55] DEBUG Austin::API::vendor_api - Initialisin
+g the API Galileo
[2008/10/14 10:57:18] [41] DEBUG Austin::Suppliers::Common::Location::
+init - Setting Up Generic Locations
[2008/10/14 11:15:22] [147] DEBUG Austin::Controller::default - $VAR1 
+= {
          'Errors' => [
                        {
                          'ID' => 'noRates',
                          'Error' => 'No Rates for given dates/times',
                          'object' => '/var/website/modules/Austin/CB/
+Search.pm',
                          'Location' => undef,
                          'line' => 371
                        },
                      ]
        };
[2008/10/14 10:57:18] [245] DEBUG Austin::XV::Trip::set_time_zone - Ch
+ecking timezone with agent UK
[2008/10/14 10:57:18] [247] DEBUG Austin::XV::Trip::set_time_zone - Se
+tting timezone to Europe/London
[2008/10/14 11:15:22]
[2008/10/14 11:15:22] [147] DEBUG Austin::Controller::default - $VAR1 
+= {
          'Errors' => [
                        {
                          'ID' => 'noRates',
                          'Error' => 'No Rates for given dates/times',
                          'object' => '/var/website/modules/Austin/CB/
+Search.pm',
                          'Location' => undef,
                          'line' => 371
                        },
                      ]
        };
[2008/10/14 11:15:22]
[download]

"Also be nice if I could pipe to it also so tail -f <LOG> | log_grepper.pl.. "

#!/usr/bin/perl -w

my $targetF = "/var/log/local2";

for(;;) {
    open ML, "<$targetF" || die $!;
    #seek(ML, 0, 2); # to EOF - Not, process from beginning
    
    for (;;){
        while (<ML>){
            another_line();
        }
        sleep 2;
        seek(ML,  0, 1); # reset end-of-file error
    }
    # dropping here with the 'last' should cause
    # the file being monitored to be closed and reopened
    close (ML);
}

sub another_line {
    # $_ has the line
    # Check for target phrases
    return;
}
[download]

But any cyclically incremental reading of the file adds the need for accumulation of multi-line events, handling partial (incomplete) lines, and all the other 'streaming' techniques.