As I go through the appraisal I have already noticed some discrepancies that I will respectfully be updating the lender with.  

Then it’s just a matter of comparing your sample data to the deals you’re analyzing and looking for large discrepancies.

I did spoke to a city inspector and he said the property needs to be signed off on all discrepancies within a few month after closing of escrow.

We want to put in an offer due to this discrepancy, but what is the right way of starting this process?

Those usually give you easy discrepancies to point out.

If there are substantial discrepancies that will disqualify the tenant, I usually let the tenant know that their background check revealed issues.

Just bringing contractors in to give a bid by walking around and having them come up with the work being done will end up with massive discrepancies (as you are seeing).

To further this, I went to 6 hml, 3 said they wouldn't make an offer due to discrepancies in valuing the subject property- it was a 4700sqf older build (1975 Georgian) in a neighborhood of 2.5k-3k similar age properties and a few blocks away a small section of 3k-3.5k new builds.

So in my due dilligence for wholesaling and looking up comps for my list of properties, there have been a few of them where googling the comparable property to find info pulls up different information on different RE ...

If the home has been vacant for a while, it is likely that discrepancies will show up.