"Grounds" is not the subject of the verb "to be", but the complement -- like an object, except that the complement is also the subject: the verb "to be" acts like an equals sign:
Sleeping on the job = grounds for dismissal
No matter what the complement is, though, the verb agrees with the subject. "Sleeping or appearing to be sleeping" is actually singular (logically, because we mean one or the other, not both), so "was" is correct here.
All the same, "grounds" is plural -- "There were sufficient grounds for his dismissal". It does often refer to something singular, but we're talking grammar here, and grammar doesn't always match up with real life.
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