Final answer:
The sentences provided do not contain any significant usage errors. The only possible correction is a capitalization error at the beginning of the third sentence, where 'We' should be capitalized.
Step-by-step explanation:
In examining usage errors in the provided sentences, it appears that there are no conspicuous grammatical errors within the sentences:
That shop is where you can buy rare shells.
They are anxious to see their new grandchild.
We expressed some doubts as to his competence.
Each sentence conveys a clear meaning and adheres to the rules of standard English grammar. Considering the subject matter and requests in the instructions, there is no need for correction in these examples. However, there is the possibility of a typographical error in the third sentence, as it begins with a lowercase 'w' instead of a capital 'W'. This error would be corrected in formal writing to properly begin the sentence with a capital letter:
We expressed some doubts as to his competence.