I had quite some trouble finding a stupid error in my Search API setup. Here is the rule:
Don't activate a fulltext field as a facet - otherwise you'll get an error on each search page!
Here is the error, which in retrospective make a bit sense:
SQLSTATE[42S22]: Column not found: 1054 Unknown column 'value' in 'where clause'
It seems as Facet API i always looking for a value column, no matter of what type the indexed field is.