Is It Wise For A Married Man To Compliment A Woman - Regarding Her Looks / Attire - Who Isn't His Wife (Regardless Of This Lovely Woman's Marital Status)?

It is unwise.  Do not do this.  Even if you're friends with the woman, work closely with / supervise her within a vocational / volunteer setting, etc.  Even if her attire / looks is / are extraordinarily beautiful / attractive to you or you as a married man are much older than her, and therefore you see her more as a daughter.  Do not do it.

Just don't.

And on that same note, never, ever write her a thank you note for a job well done.  Instead, compliment her face to face but with other team members / supervisors present and be very specific as to what she did so well within your eyes - as her supervisor from you as a supervisor with a supervisor's point of view.

Hopefully, you catch my drift here relative to how easily your words can be misconstrued.

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Why?

Women are not equal to men.  They see the world very differently than we do.  And this is a good thing.  Thanks be to God for women.  

Therefore, because of this truth, we as men must be vigilant to not misconstrue or take advantage of - in any way - that inequality.  As men, we have an obligation to women to be extraordinarily mindful of our responsibility to them and their differences and never assume otherwise.  And this starts with both our words (or lack thereof) themselves and how we choose to deliver (or not) those words, but ESPECIALLY WHEN these women are not our spouses.

I speak from experience, having learned the hard way regarding my man mouth.