I tunes playlist

There's no one, definite answer, as there may be more than one reason. Let's try to eliminate any possible causes, one by one. I suggest that you use the Songs view for these tests, as it makes it easier to see messages, errors etc.

• can you identify any specific song that doesn't play? If so, what happens if you double-click on it, to force iTunes to play it? If it doesn't play, are there any error messages?
• are there any indicators next to the song, such as an exclamation mark to the left of the song's title, a cloud symbol perhaps?
• are you using Shuffle mode? If so, try turning it off. Does that make a difference?

One more thing; I notice that you refer to a playlist. Are you playing a playlist that you've made, a built-in playlist prepared by iTunes, or are are you playing from the complete songs library?