The job belongs to last year as it was, so it is a possessive. So there is an apostrophe needed between year and s, so it does not indicate a plural. The correct form is:
Last year's job.
the spelling "person" is correct (an individual).
The correct spelling is referral (job recommendation, or medical submission).
That is the correct spelling of "rotted" (putrified, or crumbling away).
The correct spelling is "full-time" with a hyphen when used as an adjective, such as in "full-time job." When used as a noun or adverb, it can be written as "full time" without a hyphen.
That is the correct spelling of "Christmas decorations" (trees, lights, ornaments, wreaths, garlands, mistletoe).
The correct spelling is "assigned" (given as a task or job).
That is the correct spelling of firefighter (from fireman).
Jobs.
That is the correct spelling of "job share" (also job-share) also phrased as "job sharing."
That is the correct spelling of "work" (energy expended, or a job).
The correct spelling of the verb is employ (to utilize, or to provide a job).
the spelling "person" is correct (an individual).
The correct spelling is strengths. The job applicant had to list his personal strengths.
The correct spelling is second. (either the unit of time or 2nd in order)
You need to correct your spelling errors. Employers will not respond to resumes and cover letters that have spelling or grammatical errors.
That is the correct spelling of "tackled" (in sports, brought down; or attempted a job)
The correct spelling is referral (job recommendation, or medical submission).