I believe that there is no right or wrong way to how a DJ play's the music generally speaking.
There are some NEGATIVE things that a DJ can certainly do though:
1. Letting a song end, and going into "DEAD AIR" before the next song start's to play during a set-----> BAD...VERY BAD. Probably one of the worst things a DJ can do outside of screwing up a bride/groom's first dance, or introduction, or totally butchering the names of people in the bridal party on the microphone. May not be as bad as having a terrible sounding sound system making awful noises or distortion all night long. Playing onoxiously loud is another bad thing a DJ can do that may be worse than some dead air in between a song.
2. Showing Up Late/Starting Late. ....Yeah, I think that would be worse than some dead air after a song.
3. Not having the important music that needs to be played. ....Yup, I would consider that worse than Dead Air.
So, after all of that, and some other stuff I'm probably not thinking about, comes how the DJ mixes.
There are clientelle that want music played, and prefer for The Full song, or 90%+ of every song to be played. There are also clients that like a great sounding mix, but want to have a good amount of time to enjoy each song. ...Those clients may find that a DJ mixing in and out of songs every 2 to 3 minutes is putting on a GREAT show for them. ...Then there are other clientelle out there that really loved when a DJ is mixing in and out of songs every 20 to 60 seconds, and enjoy that FAST club style mixing.
Generally speaking, DJs are going to mix firstly by how they were taught, or how they learned. 2ndly, DJs are also going to play music how they listened to it.
My Dad is 74. He plays the full songs, and mixes into the next song near the very end of the song. That is how he has always been. He will only change into another song early if a song is just not working. The older crowd Age 55+ PREFERS the full songs. They won't like a DJ mixing songs every 20 to 60 seconds. They like to take their time, and enjoy the full songs. THEY ALSO GENERALLY KNOW HOW TO DANCE TO MUSIC. ...The younger crowd doesn't KNOW HOW TO DANCE. ...SO the younger crowd out there will like song changes much faster because they can't keep their excitement level up during a 3:30 to 5 minute long song these days.
So Taso is Correct. ...Deejaying for the Sweet 16, and young 20 something couples getting married crowd will generally WANT faster mixing. Now with weddings, they WILL want to hear MOST of certain songs...not just 20 to 60 seconds of it. It's up to the DJ to figure out what those songs are where the crowd will want to hear and dance to most of the song. ...I can name at least 15 to 20 songs off of the top of my head I would never just play 20 to 60 seconds of at a wedding. But there are others where I would not want to play the full song either, and mixing in and out of those songs is key.
I do believe Drax is correct gnerally speaking though. School Dances, Sweet 16s, College Age events. Those events really do need fast in and out mixing of songs to keep those crowds satisfied. They are not really interested in hearing "the full length" of most music. They will want to hear most of a anthem type, or sing a long type song, but most dance/hip hop/rap....need to mix quickly to keep them involved, and liking your performance these days.
Age under 29 wedding clients: They will generally want more of the fast mixing...Especially when the party really get's going, and most of the crowd is Buzzed on alcohol. Playing full songs for this crowd may leave a lot left to be desired
Age over 29 and under 40ish wedding clients: They will generally be fine with a DJ who plays 2 - 3 minutes of each song, or even plays 90%+ of each song. This can vary a little bit depending on if the clients were/are big into going to clubs in urban areas or not, and want that club feel or not. Playing full songs is probably fine as well as long as the transitions are seamless, and we are talking a wide age range of guests.
Older age group Weddings, 40th birthdays, 50th birthdays, 60th birthdays, Anniversaries...They don't care about a DJ fast mixing. They may not care at all how the DJ mixes. They just want seamless music, and a good overall time.