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Slippery floors. Have two pairs of table tennis shoes. Most table tennis shoes are designed with a normal floor in mind, and that's where they should be used. Some of the Chinese table tennis shoes are almost too grippy on these same floors, making it hard to move with them (look for shoes with "suction cup" soles). However, these are perfect for those slippery floors. Bring both types of shoes, and you won't be the one ice skating during your match.
Second solution: put a slightly wet paper towel on the floor, and step on it between rallies. This will make your shoes extra grippy, but only for a minute or so. It's a hassle, and since the friction between your shoes and the floor isn't a constant, it can be tricky to move. That's why I recommend using two pairs of shoes. (Few top players have to deal with this problem because they rarely play on slippery floors. Many of you have probably seen the special red floors used for the championships events at the U.S. Open, U.S. Nationals, U.S. Open Teams, and many 4-star tournaments. Top internationals from Europe and Asia, of course, play only in top conditions.)
Humidity. Use two towels, one for you, one for the ball and racket only. The towel you use for yourself will get damp rapidly, and will be useless in drying off your racket or the ball. Have extra towels to replace these when/if they get damp.
Related tip: if your racket is dirty (and thereby loses some of its grippiness), wash it off quickly during a match by simply blowing on the surface to slightly dampen it, then wiping it with a towel.
Food & Drinks. Bring fruit, light sandwiches, and other food items that are high in carbohydrates, but not too high in sugar. Eat small amounts throughout the tournament rather than periodic large meals, although you should have a relatively large, high-carbohydrate breakfast. Drinks such as Gatorade.