Where do professional dues and liability insurance required for my job go, under Employment Expenses or later under Deductions?

Liability insurance is also deductible on the same line as mentioned by TonyC1.  For more info, please see http://www.cra-arc.gc.ca/tx/ndvdls/tpcs/ncm-tx/rtrn/cmpltng/ddctns/lns206-236/212/menu-eng.html

Bona Fide professional dues, those required to maintain your professional standing for employment reasons, would be entered on line 212 of the T1 as a deduction from income.

Liability insurance is another matter. It can be claimed as a business expense if you areo self employed.

where exactly would you deduct it as a self employed person?

It would be on your T2125 form.