Select all the songs in the playlist, right click on them and select "get info" (ignore any warnings about editing multiple tracks) lick on options and put a tick in "gapless album and make sure the drop down menu next to it is set to yes.
if that doesn't work as you want then you can also try enableing the cross fader which will try and fade between each track, look on the edit menu > preferences, click on the playback tab, put a tick in "crossfade songs" and play about with the slider to see which setting gives the best results.