This query...

SELECT Id, CreatedDate, Category, Message FROM ProcessException WHERE CreatedDate = TODAY

...appears to get the correct rows but the Category field is missing. This does work correctly in the Dev Console. 

This message also pops up: Warning 1 Message: mismatched input 'Category' expecting {AVG, CONVERT_CURRENCY, COUNT, COUNT_DISTINCT, FORMAT, MAX, MIN, SUM, TO_LABEL, CALENDAR_MONTH, CALENDAR_QUARTER, CALENDAR_YEAR, DAY_IN_MONTH, DAY_IN_WEEK, DAY_IN_YEAR, DAY_ONLY, FISCAL_MONTH, FISCAL_QUARTER, FISCAL_YEAR, HOUR_IN_DAY, WEEK_IN_MONTH, WEEK_IN_YEAR, CONVERT_TIMEZONE, DISTANCE, '(', Identifier}, position 24 C:\Users\DaveDurant\Documents\The Welkin Suite\Projects\Andersen - Production\Andersen - Production\Soql\ProcessException.soql 0 24