I want to know what is wrong in the following sentence:

After six months on the job, he faced problems in his first recruitment effort; however, if he solves these problems, the new hires should be able to start working by July.

You have switched verb tenses.

http://grammar.ccc.commnet.edu/grammar/consistency.htm

hires sounds a little awkward. i think hirees should be placed in there instead of hires

In the sentence you provided, there are two issues that can be identified:

1. Subject-Verb Agreement: The subject of the sentence is "new hires," which is plural, but the verb "should" is in the singular form. To maintain subject-verb agreement, the verb should be in the plural form "should be able to."

2. Tense Consistency: The first part of the sentence is in the past tense ("After six months on the job, he faced problems in his first recruitment effort"), indicating that the problems occurred in the past. However, the latter part of the sentence is in the future tense ("the new hires should be able to start working by July"). To maintain tense consistency, the verb tense in the latter part should also be in the past tense.

To correct these issues, the sentence can be revised as follows:
"After six months on the job, he faced problems in his first recruitment effort; however, if he solves these problems, the new hires will be able to start working by July."