Calibri seems to look nice though I prefer Arial.
I've added Calibri to the page. (maybe it worth writing some script that changes fonts on the fly since the page gets too long. :-))

Will this test page help?
http://jplangtools.com/tatoeba/fonts.html

> Can you tell if Tatoeba's thinspaces are really thinspaces or the narrow-no-break-spaces they really ought to be?

Absolutely not. To tell the truth, I don't really care if some space is thin or not-so-thin or if some dash is long or not-so-long. It doesn't prevent me from understanding the sentence. :-)

Isn't it strange? :-)

This is the page that demonstrates Uyghur sentence rendered using different fonts:
http://jplangtools.com/tatoeba/national.html
UKIJ fonts are being uploaded via CSS on the fly and the other fonts are those the OS contains. There are also "sans" and "sans-serif" lines included so one can see what font his browser actually uses to display those typesets.

Charis SIL font is really great but it's too big in size to be downloaded on-the-fly via CSS. So one have to install it manually and this may be a problem.

As for my Chrome on Windows 7, Hebrew sentences looks like this:
http://dl.dropbox.com/u/42772287/Hebrew.png
The same is with Arabic.
What a mess! :-)

Nice page, by the way!
I've made a test page based on it.
http://jplangtools.com/tatoeba/spaces.html

> It would also be nice to right-align languages that are read right-to-left, but that's probably asking for too much, eh?

Actually, in Gecko-based browsers (Firefox, Seamonkey, etc.) RTL sentences are displayed right-aligned. But it seems this doesn't work for Chrome for some reason.

It's possible that a localization of particular OS version also matters. And, possibly, the service packs installed, too.

hmmm... actually, W3C did its best at providing various types of HTML entities (see http://www.w3schools.com/tags/ref_symbols.asp ) but all that stuff is more for the coders, not for the end users. Older operating systems seems to have limited support for Unicode and, unfortunately, W3C can't help it.

Browsers running on Windows 7 OS seem to work like a charm. My Dolphin brobser (WebKit based) that runs on my Adndroid 4 device displays 1,2 and 4 lines correctly, too.

Now I clearly see that the problem is more complex than it seemed. We have to take into account not only the browser type but also the operating system type and version.
The most universal solution is to use HTML entities instead of Unicode symbols. The problem is that this requires on the fly conversion inside the Tatoeba engine.

Please take a look at this test page:
http://jplangtools.com/tatoeba/thinspace.html
What do you see in your browsers?

You're absolutely right. But we can't and we shouldn't rely upon browser font configuration, neither default not user made. Default configurations may be not optimal (read "ugly") and a user may have no idea how to change it (and, actually, many if not the most of users just don't suspect that font configuration exists). That is, talking about Tatoeba, it's necessary to determine what font family is best to display this or that alphabet and explicitly instruct browsers through CSS to use it.

UKIJ fonts were taken from here
http://www.ukij.org/fonts/
There are a lot of other fonts there.

I've created a simple test page that displays http://tatoeba.org/eng/sentences/show/2125035 using different fonts:
http://jplangtools.com/tatoeba/tatoeba.html

To my untrained eye, there are no much differences :-)

Btw, as halfb1t noticed, sans-serif (as well as serif, monospace, etc.) is not a font itself but rather a typeset. Usually, it can be changed in the application settings to any font you like best.

It seems that Tatoeba uses Georgia (belongs to serif typeset) font for displaying main sentence. I'm not sure if this particular font contain all Unicode characters, so browsers may fallback to the font of last resort displaying non-ASCII characters. As different browsers use different font rendering engines, the effect will differ from one browser family to another. In particular, in WebKit based browsers and in the ones based on Gecko the same text will look different.
The only way out I see is to use different font families to display sentences in different alphabets, though it may be kinda tricky task.

はい、そうですね。＾＾
You're were the 1st Tatoeba Japanese member to respond in the New Year. :-) Unfortunately, there are not much members from Japan here. If you know people in your country who might be interested in participating the project, please encourage them to join us! :-) ありがとうございます。＾＾

С Новым Счастьем! :-)

The new 2013 year is coming to Japan in 4 minutes!
To our Japanese members:
新年おめでとうございます! ＾＾
Happy New Year!

We're at the Tatoeba, don't we? So
http://tatoeba.org/rus/sentences/show/844267
:-)
By the way, the Orthodox Christmas will be celebrated on the 7th of January, so we'll waiting all of you back this day :-)