Generally speaking, I see two peculiarities (or rather tendencies) in Russian phonetics that can complicate the matter for a non-native speaker (and even for native speakers who want to speak standard Russian):

1. Unsharp articulation of vowels

1.1 weakened artucilation in unstressed position

/o/, /a/: [a] next to the stressed syllable, [ъ] in other unstressed positions.

/е/, /и/, /ä/: [и] next to the stressed syllable, [ь] in other unstressed positions.

/ы/: [ь] in unstressed positions other than next to the stressed syllable.

1.2 Unclear articulation in some other positions.

/o/: often [yo] like in полный. Believe it or not, but the glide here is even weaker than it's Lithuanian counterpart.

Please note that sharp and clear artucilation considered to be extremely unnatural and indicates non-native speaker. For those unexposed to the Russian phonetics: please imagine the language where paradigmatical and word-formation changes throw the stress back and forth much more inconsistently than in, eg., Lithuanian (cf. the number of accentuation paradigms, an important difference is, of course, simple expiratory stress in Russian) and cause consequent changes in half of the vowels in the word, two of them being 'schwa' and 'palatalized schwa' (could comebody help me with IPA symbols for [ъ] and [ь]?).

2. 'Soft' (semi-palatalized) : 'hard' (unpalatalized) versions of consonants. Of course this opposition is not pertinent to Russian only, the zest here is that, for instance, palatalized dentals stand somewhere between semi-palatalized Lithuanian and over-palatalized (up to the affricates) Polish. Thus, my Lithianian-speaking wife can hardly render such important Russian word as дети 'children', falling either in Lithuanian dė- or Polish dze-.