Can an EEG show an abnormality that is not epileptic in nature?

Yes. Eeg abnormalities can be seen in depression, migraine, medication, and other non seizure diagnoses. The neurologist is to determine if this suggests epilepsy or not.
Quite frequently. The eeg is a crude measure of brain electrical activity. It often also contains events of eye movements, swallowing, breathing, movement, as well as outside electrical events including lightning. It is very important for the neurologist evaluating the eeg to be knowledgable about all the possible artifacts and variations. Eegs on children are very often full of such non-epileptic events.