After almost two years of moderate usage I encountered lack of one of useful feature of the standard grep: prepending line numbers and file names to the output. This night I decided to close this issue and implemented the absent functionality. By the way I turned on auto flushing as well. Please meet the updated version and use/test it if you want :)
# print line numbers
paragrep -n PATTERN FILENAME
# print file names
paragrep -H PATTERN FILENAME
# suppress printing file names
paragrep -h PATTERN FILENAME...
Later, if none of us discover any bugs, I update the initial post with the recent version of the script.
The script lives on github by the link
https://github.com/ildar-shaimordanov/perl-utils/blob/master/perl/paragrep.