It is embarrassing to be caught mispronouncing an aphonetic(?) word whose pronunciation is not intuitive. Are there any comprehensive word lists (may be the 5000 popular words that are commonly mis-pronounced) or resources for a non-native English speaker that can help with the correct pronunciation of "irregular" words.
This has been bothering me as well, but for other (non-English) languages I'm studying. As @ObiWanShanobi points out the International Phonetic Alphabet (IPA) can be very helpful if you can get comfortable reading the somewhat obscure symbols.
But far and away the most useful resource I've found for pronunciation is Forvo which has Geotagged recordings of native speakers saying thousands of words. Currently English is one of the well-represented languages with 100,000+ recordings from all over the world (UK, US, etc.).
The Google Translate speaking functionality has a voice that is unnatural sounding (don't copy the intonation!), but can be helpful for hearing inflected forms (where Forvo is not as complete).
Besides that, I think speaking with patient/willing friends is the ideal situation.
AmE orthography does not always lend itself to intuitive pronunciation. That much is true.
I would recommend gaining some familiarity with the International Phonetic Alphabet (IPA). With this knowledge, pronunciation guides will be more explicit in indicating exactly which English phoneme is expected. Nearly all resources will expose an IPA translation of the word that looks something like this