This is a difficult question because except typical grammar mistakes (in endings of adjectives, for example, or absence of vowels at the end of the nouns of feminine gender), most mistakes are of phonetics field.
Some typical are absence of soft "l" (большой - could be pronounced as балшой, малчик instead of мальчик). The soft consonants pronunciation is probably the most noticeable mistake, like instead of неправильно could be нэправильна, нэт - instead of soft нет. That is why some Georgian children studying Russian try to say the consonants in a soft way by adding "j": [njet] Besides, instead of soft consonants like "щ" can be pronounced [sh].
The linguists write about more "closed" vowels (a, e) in Georgian vs. very opened ones in the Russian language. I read that it can be explained that in the Georgian language there is no such category as softness and hardness.
The above mentioned is connected to the following. The sound combinations like in the letter "ю" can be simplified to [u], for example, "сюрприз" can turn into "сурприс"
Moreover, in Russian, the vowels are sounding differently depending on their position from the stressed vowel, while this is absent in Georgian. For example, молоко with the last vowel stressed, will be [malakO] In Georgian language, the vowels when they are not stressed are pronounced more distinctly then in the Russian phonetics.
Also, in Georgian language, there are some aspirate consonants not existing in the Russian language so there is a tendency to pronounce the consonants like "ч" and "х" in aspirate-type ones.
Besides, there is a tendency to move the position of stressed vowel to the beginning of the word.
