Parts of the following sentence are given as options. Identify the segment that contains a grammatical error.

Mr. Bansal is the more methodical person in our office staff.

The correct answer is 'the more'.
Key Points 

• The given above sentence is grammatically incorrect.
• The given sentence is an example of the superlative adjective.
• Superlative adjectives are adjectives that compare the traits of three or more nouns.
• As per the general rule, we add the definite article 'the' and add 'most' to adjectives that have 3 or more syllables for the superlative form.
• Let’s have a look at the structural form of the given rule:
  • Noun (subject) + verb + the + superlative adjective + noun (object).
• Example:
  • expensive– most expensive
  • difficult – most difficult
• ​Example in a sentence: 
  • ​One of the most appealing things about Alex was his confidence. (correct)
  • One of the more appealing things about Alex was his confidence. (incorrect)
• ​Here, in the given above sentence, 'the more' is used as a superlative form, which is wrong according to the rule.
• According to the explanation that is given above, ‘the most’ is the correct use in place of “the more”.
   

Correct sentence: Mr. Bansal is the most methodical person in our office staff.