"The operator has a responsibility to record / take record of any complaints and concerns brought up by users."

Personally, I'm not sure "evidentoj" is the best term to have been used here. But according to the dictionary:

EVIDENCË f. sh.
1. zyrt. Shënime ose të dhëna që mbahen
në një fletë letre a në një regjistër, të cilat
pasqyrojnë gjendjen e punëve a të
veprimtarisë së njerëzve, të ndërmarrjeve,
të institucioneve etj.; vetë fleta e regjistri ku
mbahen shënime të tilla; pasqyrë. Evidence
ditore (javore, mujore, vjetore). Evidencë
ekonomike (statistikore). Evidencë
ushtarake. Evidencat e detyrimit shkollor.
Hap (plotësoj) evidencën. Mbaj evidencën.
Vë (fut) në evidencë e shënoj, e regjistroj.
Heq nga evidenca e çregjistroj. Marr në
evidencë e regjistroj. Hyj në evidencë
regjistrohem. Shënoj në evidencë. Mbaj në
evidencë e mbaj shënim, e shënoj që ta
kem parasysh.

-- it plainly means to officially put something down in record .

The other two given answers have slightly different uses.

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Note added at 2 days10 hrs (2008-01-31 20:18:40 GMT)
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Just a little note on why I am neutral on the use of "register" and "document" in this particular case. When I googled the phrases, all the hits that came up were about the consumer filing a complaint in a way or another, as you can see in these links:

http://www.google.co.uk/search?q="register a complaint"&hl=e...

http://www.google.co.uk/search?hl=en&q="document a complaint...

The missed point here is that we are talking about a complaint being taken down by a person who has the official job to do exactly that. This is why you can't have an indivual take a complaint in record, but file/register/document it and the person in charge in the other end will record it, that it is to say, put it through the system so that it results as a statistic in the least and is on the way to be dealt with.
Just the way I see it.

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Note added at 7 days (2008-02-05 14:37:37 GMT) Post-grading
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I want to thank everyone for their input with this term and can understand why it would prove to be so contentious. For starters, there is no dictionary entry (if there is, someone please provide a reference and I'll stand corrected :) and update mine). Although it is being used heavily across the media, I have e feeling that everyone is freely adapting it to mean different things at different times, and I have found some articles that provide evidence for its alternate meanings:

"Nuk them ndonjë gjë të re po të evidentoj faktin se pak vëmendje i është kushtuar në Shqipëri çështjes së mbajtjes së statistikave gjyqësore. ...
-- vë në dukje –

“Ndër problemet që unë evidentoj kanë lidhje me bujqësinë dhe industrinë me këtë zonë. ... Aktualisht unë evidentoj si problem dhe mendoj se duhet të ndërhyj ...”
-- dalloj / vë re –

“I përmenda këto me qëllim që të evidentoj që femrat me vullnetin dhe punën e tyre janë shumë të suksesshme dhe të respektuara në shoqëri duke marrë vendin ...”
-- dëshmoj/paraqes fakte --

In our case, I think we've probably run yet into a poor translation and we're all trying to figure out what the operator was meant to do originally. It may well be that Nick is correct with his answer, but I wouldn’t say that source test is undisputable - certainly Albanian texts are mind-boggling (to say the lesat) at times, but there are plenty of English monolingual questions here in Proz that would stand in favour of dispute. However, I am in favour of a more light-hearted approach, especially for a non-pro question.