Other people may misinterpret my "calming my mind"

What can I do to keep people from thinking something's wrong with me just because I don't get wildly emotional at every little thing?

Practice expressing brahmaviharas explicitly. It will help others to see that your calm demeanor isn’t based on indifference.

Just make sure that you only say what you mean. If needed, metta bhavana can aid in deepening your compassion for others, and will not interfere with your ambition to develop stillness.

Whether or not you are an "offical" Buddhist, you are a human being. Any human being who reacts wildly with emotion or does not react at all is a human being with problems. And almost all of us fall within these two categories most of the times.

Being a Buddhist (offical or not) or having a calm mind does not mean that one does not have or express any emotion at all. In fact you can find many stories where Buddha, Boddhisattvas, Arihants express great joy and are blissful and show great empathy. Having a calm mind means that one acts in accordance to the sitaution; one acts- doesn't react. That is, having a calm mind means that if it is a jouful/happy ocassion, one is happy without loosing the balance of the mind (becoming madly ecstatic). Or if it is a remorseful situation, one is empathetic, without becoming overwhelmed with sadness oneself. The balance of mind, avoiding the extremes of emotion (too much or not at all) is important.

You cannot do anything about what people think of you. You can do everything about your balance of mind, your calmness of mind. For that you dont need to be an offical buddhist. Being over-emotional or a lack of emotion are both dangerous. There are good emotions to cultivate like loving-kindness, warm heartedness, joy etc. Cultivate your wisdom and balance of mind- then you would be, in every situation, calm and happy. You wouldn't feel the worry of what other people think of you. That is a benefit of such positive emotions.

In Buddhism, calming the mind, if done sufficiently, eventually leads to joy. Joy is an excellent basis for developing another practice called 'metta' ('good-will'). Also, the calm mind is sensitive to the suffering of others, therefore the calm mind is an excellent basis for developing 'compassion' ('the hope others are free from suffering' called 'karuna'). Buddhist practitioners train in both calming the mind and metta-karuna.

What can I do to keep people from thinking something's wrong with me just because I don't get wildly emotional at every little thing?

Buddhism recommends what's "praised by the wise" and being inoffensive.

Perhaps try to be like a good parent or teacher -- or a mature adult, a reasonable human being, perhaps somebody with high "emotional intelligence" or a great deal of courtesy? I say that because, for example, if you manage young children then things will happen -- they get upset, they hurt themselves, they might hurt each other if you're not careful, they don't self-regulate as much as adults do (self-regulation is a learned skilled). And their parent or teacher is (I think) meant to be sympathetic and loving (at least they in conventional society that I know) -- and practical, and probably highly moral especially if you're a teacher (and not, "convicted of a serious crime") -- without getting too upset themselves when a child is crying about something.

Specifically-Buddhist doctrine on how to relate with other people seems to be to pratice the brahmaviharas when you're in company. There are several articles about that here. I think it's evident in standard Buddhist interpersonal messages like "may you be well".

If you don't mind my posting it here I admire this lecture (it's not Buddhist) which illustrates various forms of speech and how/when they're proper in different situations.

Possibly you shouldn't "hold your reactions in check", I don't know? But instead express loving-kind reactions. Perhaps a characteristic of well-enlightened people is that they trust themselves to act appropriately, and so they allow themselves to act.

Then again I sometimes read of stories like Is That So?, the guy doesn't seem wildly emotional to say the least, but he seems trusted or respected by his neighbours, and acts appropriately even though he says not much.

I think people appreciate it when there's some two-way communication (I once heard someone define "communicative" as, something like, "receptive" plus "responsive").