Other things I frequently see are checks for the connotiations of names, phrases, and idioms. Just to give you a cutesy example, one thing to watch out for is stuff like "To each their own". Innocent phrase, right? Yeah, sure, except that the German version is also on the door for the KZ Buchenwald, and thus has a Nazi connotiation. That cutesy little phrase, used completely innocently, can lead to a PR disaster.
Happened to Peek Cloppenburg, just this year.
To be fair, that's the first time I've ever heard of any controversy regarding 'to each their own', and I check facts, phrases and captions in UK publishing all the time. I can't find any major English dictionary/reference, online or in print, that lists a problem with the phrase, it's used all the time to pretty much shrug at the end of a discussion and say 'different people like different things, and that's OK'. 'Different strokes for different folks' is a mainly US variant. I use it all the time myself and had no idea of what Peek Cloppenburg or the phrase in German even was- they don't have shops in the UK, France, Spain or the US so I'm sure many regulars here might not either.
Looking it up, I agree that use of the specific equivalent in German by a German company 'Jedem das Seine' ("to each his own") was a huge problem for Peek Cloppenburg due to their use at the gates to the Buchenwald concentration camp, but use of the equivalent in English has no such cultural connotation I can find. Mainly due to its overwhelming historical use over the centuries as a friendly and polite resignation from a potential disagreement rooted in Latin (sum cuique pulchrum est, 'to each his own is beautiful'), which is presumably also where the horrifically cynical Nazi usage of it on such horrors comes from. None of the sub-editors I work with find a problem with it's use in English either, it's been used by columnists and writers for decades since WWII.
Agree entirely that companies should be aware when adopting slogans what that slogan, when translated into a different language or used raw, means in each market and context it's deployed in though. I don't think a UK clothing company adopting terminology from various atrocities of Empire would be a good PR move either. If a UK company wanted to put 'to each their own' on a shirt, whether they translated it or not, and sold it in Germany, that would absolutely be something a fact-checker should be looking at too.
I'm more surprised at something slipping past quality control for manufacturing for an international retailer with 14,000 staff than I am whoever is running a twitter account though. The problem with the latter is often a lack of eyeballs looking at how the company is represented, fond of the reach it gives a small PR department on a limited budget but with little quality control. That seems to be how twitter causes the end of a lot of careers, an almost unlimited capacity for damage with little oversight, due to it's nature being cheap, fast and irreverent, which is kind of social media in a nutshell and how companies want to be seen as friendly, funny and approachable, yet a single mistake by one individual can cost them dearly.
