It depends on how far along you are - if you can get through the steps, lead (or follow?) well enough, but some technique breaks down, I'd say it's time to attend social dances. No one is sitting around with a clipboard scoring your technique, you'll be able to practice connection, and eventually you'll find your technique coming back to you.
Slowing the music down is fine, but you should spend at least some time at each practice dancing to full speed music... there's no other way to train your muscles to do the technique (which you're perfecting by going slow) to full speed.
You might consider finding a practice partner, too, so you can practice dancing with someone to fully speed without the pressure of a social event - messing up is expected, because you're practicing and doing things out of your comfort level.