Our first cruise on the Royal Caribbeans Mariner of the Seas was absolutely awesome - and has set a high level of expectation for our next cruise. In spite of the huge number of passengers to deal with we found all the staff extremely helpful, willing to assist and very courteous. The ship itself was fantastic.
Obviously with the large number of people on-board (and trying to embark/disembark) there will be the usual delays (so get over it or get used to it!).
In spite of all this, we found that the organization was very well done under the circumstances. We went on a different port excursion every day and found it no issue on finding out what/where we had to be and directions to get to and from. The excursions themselves were well organized and we were truly looked after. Our guides were very conversant and all of us enjoyed the time ashore. Hint: Book excursions before you get on board - or prepare to wait in a very long line.
Food, entertainment and facilities were above what we expected. We didn't do half the activities on the ship we planned to do due to our excursions (and large amounts of time spent around the pool drinking cocktails or beer) but at no stage did our kids come back with the usual "Are we there yet?" or "I am bored". I would do it all again tomorrow if I had the chance. Made some great short term friends on board - both other guests and some very outgoing staff members.
Be prepared to wait occasionally in line. If you are naturally impatient then maybe booking a private island is for you!
As in our case, if you go into another foreign country - be prepared that there may not be a public flushing porcelain toilet on every corner (maybe you should stay on the ship - or learn to hold it?)
If you want a cabin that is the size of your house then either book one on board and pay for it - or make mates with a millionaire friend who has his own ship. Don't whinge to all in earshot.
Be prepared for some on board costs - especially if your kids spend time in the Amusement Arcade or eat/drink large amounts of foodstuffs out of the mini bar (you can always leave them at home!)
In all all - a great cruise and can't wait to go on our next.