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Sage delegates treatment of 'limit' expressions to Maxima. When Maxima has questions while evaluating an expression, it asks the user. Here: Maxima tries to compute the limit of a product as the product of limits, and is stuck because one limit is infinite and the other is zero. So Maxima is asking you what to do from there.

When Sage delegates a computation to Maxima and Maxima asks for user input, as above, in some cases Sage can figure out what the question is, and tell you about it, for example if you need to specify the sign of some variable. In other cases Sage cannot make a good enough guess of what Maxima is asking or complaining about, and it will either hand you Maxima's question as is, or keep the expression unevaluated.

Apparently in the version and mode of Sage you are running, it hands you Maxima's question, while in the version and mode of Sage I'm using, it keeps the expression unevaluated. This might be due to some change in the interface between Sage and Maxima in recent versions, or have to do with how Sage is used (command-line vs notebook vs IPython notebook).

I tried with Sage 6.2.beta5 and 6.3.beta5, both in command-line and notebook, and always got the expression back, unchanged.

sage: version()
'Sage Version 6.2.beta5, Release Date: 2014-03-23'
sage: limit(((x^(2*x)-2*factorial(x)+x*log(x,10))^((x^(2*x))/factorial(x)))/(x^(((2*x)^(2*x))/(factorial(x-1)))),x=infinity)
limit((x^(2*x) + x*log(x)/log(10) - 2*factorial(x))^(x^(2*x)/factorial(x))*x^(-(2*x)^(2*x)/factorial(x - 1)), x, +Infinity)

I don't have easy access to Sage 6.1.1 to test on that version. When you say "my Sagemath's server web interface", do you mean you are running sage -notebook on your computer (or sage, then notebook()), or connecting to some sage notebook server on the web?