Sanitize the output of the_title() or the_title_attribute() to remove whitespace

You can replace the space to dashes using wordpress sanitize_title_with_dashes function Try below code.

 <a href="http://twitter.com/home?status=<?php echo sanitize_title_with_dashes(get_the_title(get_the_ID())); ?>.<?php get_the_permalink(get_the_ID());?>" class="twitter">

I have used get_the_title() and get_the_content() functions because these both function return the context instead of echo them, and i think you are concatenating the string.

Hope this help .