I've never been aboard Explorer Of the Seas. But, based upon my own experience with other "Voyager-Class" vessels of Royal Caribbean, you have absolutely nothing to be concerned about. These ships are kept in tip-top condition. Explorer herself is 6 years old (maiden voyage was October 28, 2000). So, go ahead and book-you won't be disappointed!
Voyager of the Seas: October 2004
Adventure of the Seas: December 2006
Anthem of the Seas: October 2016
We went on the Explorer in August out of New Jersey. It was a wonderful 9 days. The ship is fine. Out of the 4 cruises we have been on it ranks in the middle. It lacked the personality of the Enchantment but was newer and had more to do than the Majesty. Food was great but tables in the buffet can be hard to come by at times. Lots of chaise saving by the pool that was not enforced. Smoking was well controlled - better than on any of our other cruises.
Mariner of the Seas 8/07
Explorer of the Seas 8/06
Enchantment of the Seas 8/05
Majesty of the Seas 4/05
Disney Magic 8/04