I'm looking for an offline dictionary for my smartphone - Windows Phone - for, preferably, English-Esperanto. I've seen a few in the store, but I'm not sure about the quality (as in, are the words actually correct)... Could anyone give advice on the best app?
You can use any program which supports the StarDict format (I don't use Windows, please look yourself in the store).
Further, you can search for the dictionaries in the StarDict format on the internet. For example, I'm using a german-esperanto dictionary pair for both directions, which is quite good. I've also seen esperanto-russian, esperanto-swedish, esperanto-chinese pairs.
The dictionaries for esperanto-english are here
For what it's worth, I'll point out that most of the automated translation software out there regardless of the platform ranged from horrible to barely tolerable. I use Google Translate on Android from time to time. It has an offline Esperanto-English dictionary. It still needs work, but it's an acceptable mobile dictionary. However, if that's what you want, PReVo is a better choice. It's based on the Reta Vortaro, ReVo.
Now I've been using something simply called the "Esperanto dictionary". It isn't awesome, because there are no explanations. There is just a word - and this gives you another word in Esperanto. It is bidirectional, though, so that's good.
The gtongue offline dictionary offers a number of dictionaries that you have to look up yourself. Not all of them seem trustworthy (Engligh idioms, for example). There is an Esperanto-Russian dictionary among them, but I can't say much about the quality. I like that they offer the Devil's Dictionary as well. (So random!)
Kauz Esperanto-English dictionary feels a bit more like a serious dictionary, with some modern words like "legilo por inteligentaj memorkartoj". :-D