Appear

1. Typical mistake: S/he appears very angrily today. 

'Appear' has two meanings, and the grammar is not the same in the two cases. 

a. It can mean 'seem'. In this case, it can be used with adjectives, but not adverbs. 

S/he appears (to be) very angry today. 

S/he appears quite normal. 

'Appear' can be followed by a noun (subject complement), but we very often use 'appear to be' in this case. 

S/he appears (to be) a very religious person. 

b. The other meaning of 'appear' is 'come into sight' or 'arrive'. In this case, adverbs are used, not adjectives. 

S/he suddenly appeared from under the bed. 

S/he often appears unexpectedly and invites himself to lunch. 

2. Note that 'appear' is one of the verbs (like 'be', 'seem') that can have 'there' as an introductory subject. The construction is usually 'There appears to be...' 

There appears to be a misunderstanding. 

There appears to be no point in our continuing. 

'Appear' is not usually used in progressive tenses.