We have SP2013 (PREM). I have a custom list with a date-picker column and another column called "Timeslot" which is a dropdown menu of about 15 20-minute choices. The desired end state is to be able to have this form (newform) present an "error statement" such as "Please choose another timeslot" (much like a validation does) if the user selects the same exact timeslot on the same exact date as another person did so we don't have any "double booking" of these timeslots. Is this achievable OOTB SharePoint or do we need to bring in jquery? Note this is not a calendar webpart but a custom list.
If your Timeslot column were a standard SharePoint "Date and Time" column, you could set "Enforce unique values" to Yes, and if someone picks the same date/time of a list item that already has that value in that column, it will display "This value already exists in the list".
This method would not work for what I understand you currently have because it sounds like you have the Date and the Timeslot in two separate columns (correct?) You can't use the OOTB "Enforce unique values" on multiple columns.
Another, more messy OOTB way I can think of would be to create another list with all potential timeslots out into some point in the future (perhaps with a Powershell script) and make your Timeslot column a Lookup into that list. Then put a workflow on the main list that either deletes the Timeslot from the lookup list when it is taken, or sets a flag on it to say it is used. For the latter method, you would create a calculated column in the lookup list that returned blank when the timeslot was used, and use that calculated column in your Lookup. Blank values get filtered out for lookups.
Sorry if this is rambling...