The question of verification is raised when we are concerned with distortion, hence it is an important question. One way to test for distortion is to track the changes (or lack of) in a linear fashion from origin to end (historically speaking). Another way to test for distortion is to study the desired effects of the treatment. If the results or effects deviate from our desired results/effects, then we can conclude that the treatment has been altered or distorted somewhere. So as an investigator we need to know the nature of the tool (in this case the Gita) and the desired result/goal of the tool (the Gita).
Srila Prabhupada said that verification can be done through three sources; historical evidence, spiritual authority (Parampara) and one's own self realization (atma tattva darshanam).
LINEAR REFERENCING FROM ORIGIN TO END
Historical evidence (in the secular world historical literary evidence is held high)
This is a tedious process. Historical evidence of the Kurukshetra war for example has been tested through astronomical alignment of stars/planets, archaeological facts and radioactive testing (these are few i am aware of). Literature studies such as the Bhagavad Gita is tested by modern scholars by way of variations in grammatical/literary and language presentations. So as prabhuji mentioned, the Mahabharat has returned various results and considered by some as corrupted with different narrations of the same incident. This is much like the Crucifixion of Christ is narrated differently in the Gospel John versus Mathew or Luke or Mark. So scholars debate which version is correct. Strictly from a literary standpoint, due to lack of standard documentation techniques, one can expect distorted versions of the same story or incident. Bhagavad Gita in that historical accuracy sense may be distorted....the real answer - we do not know for sure. So if you are studying the Gita from an archaeologist and/or historian perspective, then you may be hard pressed to verify the veracity of each sanskrit sloka in the Gita.
VERIFICATION THROUGH EFFECTS OF TREATMENT (can be divided into two - spiritually speaking the following two are held high)
Spiritual Authority (Parampara System)
Having touched on the historicity of the Gita, still the slokas in the Bhagavad Gita is the same in all translations of the modern era dating back as late as 2000 years or so. Now if you are reading the Gita from the perspective of spiritual emancipation and enlightenment (effects of the Gita), then historical evidence is not useful. We need to test it from the standpoint of spiritual authority (Guru Parampara). The meaning, and interpretation of the Bhagavad Gita was, is and will be consistent within the Parampara system (cannot guarantee outside of it). So Srila Prabhupada comes within the Parampara system directly started by Lord Brahma leading to Vyas to Madhwacharya and finally to Prabhupada himself. While the language and contextual explanation may be unique to the commentator, however, the essence and meaning will remain intact. It is like old wine in a new botte principle. As time changes, people change, culture changes - so Prabhupada presents his commentaries to the audience he writes while maintaining the core spirit, value and essence of the Bhagavad Gita. The spirit is maintained air-tight within the Parampara system. So if you study the previous translations of Brahma Madhwa Parampara writings of the Gita with Prabhupada's commentary, you will find the meaning and essence repeating itself AS IT IS without ulterior motivations. So this is one way to test positive for the Gita.
One's Own Self Realization (atma tattva darshanam).
Another effect of the Gita is through one's own realization of the truth (tattva). This is one of the significant evidences that cannot be over stated. This is where most if not all miss the bus. While verifying the Gita based on spiritual authority is the first step to enter into the Gita Wisdom, it is by one's own realization one sustains the Gita and transmit the essence to future generations integral with the Parampara teachings. So spiritual authority and one's own realization goes hand-in-hand. In other words, great saints who are ALL self-realized "ARE" part of the Parampara system (are spiritual authorities). That is why we can say with 100% confidence that the Gita by Prabhupada is the gold standard. This gold standard is true even if you read any saint's translation who is part of the parampara system (it is not exclusive to Prabhupada). However, Srila Prabhupada's translation fits the 21st century audience, hence most appropriate. Besides, he is the one who took immense pain to spread the word of Krishna throughout the world and it is because of his pains we are currently reading this Bhagavad Gita As it is.
Through the parampara system and through the Gita wisdom itself, we can analyze who is a self-realized soul and who is not. Then based on that criteria, we judge appropriately. If we take the medicine appropriately given by the doctor as per the instruction of the doctor and the label of the medicine, then we will become cured of our disease. Although I may not know anything about the medicine itself, still i can vote with confidence that the doctor and medicine are bonafide. Similarly by practicing spiritual sadhana as given in the Bhagavad Gita (like the label of the medicine) and as given by the self-realized soul Srila Prabhupada (like the doctor), and if both the Gita and Prabhupada commentary is indeed genuine/valid, then the readers or audience must also become self-realized (much like the patient must be cured of his/her disease). This is the ultimate test. Bhagavad Gita As it is passes that test.
Thousands have turned their lives around (giving up drugs, illiicit sex, meat eating and intoxication) and lead pure spiritual lives by reading Prabhupada's Gita. There is so much evidence of this. While the US Federal Govt spends 1/3rd of its taxes (approx 1 trillion) on health, human services type issues, still the Govt is not able to solve the socio-economic issues that stems from drug addiction and intoxication and meat eating (obesity/health risks). Srila Prabhupada on the other hand successfully changed thousands of people's lives simply by the power of the words of Krishna in the Gita. Out of the thousands who sobered up, few hundred went on to themselves become self-realized.
Based on these above two points (parampara and atma tattva) we can confidently verify that the Bhagavad Gita As it is achieved its desired result/goal. To know the ultimate goal of Bhagavad Gita, please refer to BG 11.54, 11.55, 18.55, 18.65 and 18.66.