Box 14 on my W-2 contains withholding amounts for UI/WF/SWF, DI, and NJ FLI (three different taxes). However, TT says it does not recognize DI and inserts "Other not on list". It does gives me the option of selecting a possible explanation from a drop-down list. I chose the closest next thing which is SDI. This made my tax refund get bigger. Why is that? TT also doesn't recognize "NJ FLI". Should I simply choose "Other Mandatory Deductible State or Local Tax Not Listed" for both "DI" and "NJ FLI" and be done with it?

For DI (disability insurance) you can use "SDI" (state disability insurance). Because this is a mandatory state tax, it's deductible on schedule A. Hence by adding this to your taxes your deductions go up (assuming you itemize) and consequently your tax bill goes down.

NJ FLI (family leave insurance) is also deductible - I have no experience with the TurboTax NJ forms, but if there is nothing close to this description offered by the program then I suggest using the "other" category, and be sure to make a note as to what it is.