I'm trying to determiine how to figure my son's gross income. (for the purpose of determining if he can be claimed as a dependent) He earned $4175 in wages, $142 in dividends, but had $1265 in long term realized losses from the sale of mutual funds. Do I include the losses in determining his gross income? If I can include the loss, then his income will be below $3650. He meets the other criteria for a qualifying relative.

“ Do I include the losses in determining his gross income?”-->Yes. Your son’s long term capital losses,$1,265, usually offsets capital gains dollar for dollar.However, as he has no capital gain, he can offset his LTCL against his ordinary income. For example,his gross income(ordinary income) is $4,317 and his LTCL is $1,265, so his reportable income after LTCL is $3,052;$4,317-$1,265=$3,052; $3.052<$3,650. He, if he is not your qualifying child, can qualify as your qualifying relative; so you can claim him as your dependent.
“If I can include the loss, then his income will be below $3650. He meets the other criteria for a qualifying relative.”---->Correct; your son’s allowable capital loss tax deduction on his tax return for any tax year, figured on Form 1040, Schedule D, is limited to the lesser of: $3,000 ($1,500 if he is married and files a separate tax return), or his capital loss as shown on Form 1040, line 18 of Schedule D. Then yes as said above.