Horatio Caine determines the liquid in the pool to be an alkali and not an acid since it reacted with glass. Actually, hydrofluoric acid does react with glass and has to be stored in plastic vessels. And while Sodium hydroxide solution does weaken some sorts of glass, a) the reaction is not as fast as to explode the vessel on pouring and b) a crime lab would use laboratory glassware, which is inert to alkali.
Travers correctly explains you can use a flame test to discern if it is sodium or potassium hydroxide. What he then actually performs though is not a flame test, because in that, you don't heat up some sort of test strip to a color reaction but you dip a magnesia stick into the solution and hold it into a burner whose flame then turns either orange or red. (It also helps not to use a yellow flame in the first place or else the sodium flame coloration won't be noticeable.)
To neutralize the pool contaminated with sodium hydroxide, the CSI Miami team uses vinegar which contains acetic acid to neutralize the pool to ph 7.0. This is flatly impossible since acetic acid is a weak acid and sodium hydroxide is a strong base, so together they form a buffer system whose pH wouldn't drop to 7 even after adding several tanker trucks of vinegar. It might after adding a tanker truck of concentrated hydrochloric acid though.
Adding a single puny bucket of sodium hydroxide to a swimming pool containing some 100000 liters of water would not make a concentrated solution (that indeed could lead to the severe chemical burns depicted) but a very diluted solution which would just feel slightly soapy to the touch and cause a little eye irritation. Also, the bucket looks suspiciously light - if that was sodium hydroxide, it should weigh over 20 kg.
The volume of the pool is approximately 120 cubic meters. To create such a concentrated solution of sodium hydroxide - pH around 14, 40 kilos of solid sodium hydroxide had to be added for each cubic meter of Water - that's around 5 tonnes. To neutralize it with vinegar they would have to add a volume of vinegar equal to 2/3 of the volume of the pool.
The corrosive in the pool burns off all of the victim's hair - except his eyelashes.