What is the role of 清楚 in 一定要注意签订书面合同，核实清楚物业费、水费、...?
清楚 here is resultant complement for 核实 instead of adverbial, so the literal meaning is 'verify clear' (verify towards a clear result, think 'make clear') instead of 'verify clearly'.

If you have to insert 的/地/得, it should be 得 i.e. 核实得清楚, but that changes the sentence from imperative to declarative.

It's really just a figure of speech to emphasize 核实, as opposed to carry some actual meaning. The previous sentence '一定要注意...' is similar in that regard, by using 一定 to emphasize 注意.