Should I Worry About Warnings After Compiling In CX-Programmer?

There is a big difference between an "Error" and a "Warning". An "Error" indicates that it may not be compiled and that a syntax error is present in the program. These can not be downloaded. This error must be restored.
A "Warning" after compiling may affect the operation of the program. However, the program can have downloaded  "Warnings" and the PLC can be put to RUN / Monitor.

There are several warnings. Of course, not all warnings can have a negative impact in the program.
The following example shows that there is a double output used, a so-called "Double Coil" or "Duplicated output". This is also shown by the SET and RSET command or in data processing instructions in the program when multiple commands send data to the same contact. This may be correct and the warning can be ignored. The misuse of data types in an command is given as a warning.

One can determine whether these warnings should be shown or not. Click on PLC and then Check Program Options. Choose options on or off, which controls are shown for the compiles.