1. You want to get rid of the busy-wait in the client.

Currently you spawn a thread for sock_io() and a second thread for stdio_io(). Then you run a busy loop in your main thread.

You've identified that your main thread is excess. You can get rid of one thread (not the main one) by simply calling stdio_io() from the main thread rather than spawn a new thread. That is:

...;
my $thr1 = threads->new(\&sock_io);
stdio_io();
...;
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You should let stdio_io() return if the user presses Ctrl+D (Unix) or Ctrl+Z (DOS). Cleaning up the sock_io() thread when the user signals they're done is left as an exercise for you. :)

2 & 4. The first line entered by the user in the client is not sent to the server.

I'm taking a wild stab here by guessing it's a buffering issue. Turn buffering off on STDOUT and $socket. Before creating your thread(s):

...;
use IO::Handle;
STDOUT->autoflush(1);
$socket->autoflush(1);
...;
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3. Lines from STDIN have additional newlines, which may not be network newlines.

You need to chomp $msg_out before you print it to the socket:

while (<STDIN>) {
  chomp;
  print $socket $_ . CRLF;
}
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Additional question: Is learning/reading Unix Network Programming useful?

As with most things, there's a trade-off. Depth of knowledge is generally good, but it takes time. On the other hand, you could spend the time learning high-level libraries and using them to do more interesting things. It's really up to your personal preference or goals.

I started off low-level: I learned C before Perl. I wrote POE after learning about BSD sockets. I learned CGI, and now I use things like Catalyst. The novelty of low-level work wears off (for me) after about three uses.