You can execute the dialog in another process and just wait for that process to finish:

sub check_errors {
  return unless ($ERRORCHECK == 1);
  my $st = system("ask-yes-no", "There were errors. Do you want to con
+tinue?") >> 8;
  if ($st != 0) {
    # exit the program
  }
}
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And in your program:

...do stuff...
check_errors();
...do more stuff...
check_errors();
... etc.
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Update: See this article: CLI Magic: Creating basic front ends with dialog and Xdialog for more info on this approach. You may not even have to write the dialog application.