I am a qualified american English as a Second Language teacher looking for jobs in Thailand and I was curious if my non-offensive partial hand tattoo would be a deal breaker?
Tattoos are very common in Thailand, they have some of the best tattoo artists in the world. The only type of tattoo that is prohibited is one that depicts the Buddha, or, of course, any tattoo which would violate lese-majeste laws (offensive to the monarchy).
While sak yant tattoos are indeed common in Thailand, they are also associated with lower classes and criminals, and they are usually placed in locations that are not visible (back, neck etc) when clothing is worn. Visible tattoos are not common at all, and would generally not be considered acceptable for Thai professionals, I can't recall seeing any during the year and half I spent working in Thailand (in telco, not ESL).
Per the comments on this Ajarn.com thread, while they're not an absolute no-no for ESL teachers since farang get a bit of extra leeway, they will likely limit your options, particularly if they're in locations that you can't easily cover up.