This study, detailed in MedicalNewsToday.com discusses how increased screening of adults (the study was done in England) for hypothyroidism could improve the quality of life for thousands of people over the age of 50. I would encourage screening for those over the age of 40, as I was diagnosed with hypothyroidism in my mid 40's, and I am certain that before that I had a doctor who didn't know what the hell he was doing (sorry, little editorial comment there).
I am amazed at how many women my age and older I have asked if they have had their thyroid checked, and the answer is either "no, no one ever said anything about getting my thyroid checked" or "yes, but only my TSH, and since it's below 4-5, the doctor said nothing needed to be done". My doctor treats for any TSH over 2, and prefers it be lower than that (mine is nicely under 1). As always, check with your doctor!