Basically, he asserts that while the public opinion polls conducted for Iran at large were all over the place and of suspect quality (Polls ranged from Ahmedinejad +16 to Mousavi +32), polls for Tehran specifically might be more reliable.
Looking at a six-poll aggregate (which includes polls from before the June 3rd presidential debate), the polling median is Mousavi +4 +/- 4 (Median +/- MAD-based SEM), while the 3-poll aggregate (only includes polls from after the June 3rd debate) has a polling median of Mousavi +4 +/- 11.
The announced official result was Ahmedinejad +12% (51.6% to 39.4%), a discrepancy of 16 points. This discrepancy does not reach statistical significance compared with the last 3 polls (p=0.07), but does compared with all 6 polls (p=0.003).
For now, my interpretation is that the official returns in Tehran are unbelievable.
1) While the three poll-aggregate discrepancy from the result does not meet the standard threshold for statistical significance (p=0.05), it's sufficiently close so that I would count it as such anyway. The 0.05 statistical significance threshold was not given to us by God, see here.
2) There might be some confusion as to what "Tehran" is. Ahmedinejad supposedly won by 12 points in the "Oshtan" (Region) of Tehran. Yet official results show that Mousavi won Tehran (تهران ), Tehran with 52% of the vote and Mousavi + 8.66. This creates a discrepancy from the polling aggregate of only 4.66 points, a result fully within the margins of error of both the three and six poll aggregate.
It is possible that pollsters conducting estimates of "Tehran" were only polling people in "Tehran, Tehran", much like polls of New York City wouldn't include anyone from Albany in their sample. People with local expertise should speak up.
3) I can't find the Tehran poll internals in English, but based on a relatively incomprehensible translation courtesy of Google, it seems that 34.4% of respondents in a pre-election poll indicated that they would not vote for either Mousavi or Ahmedinejad.
According to the official results, only 3% of voters in the Tehran province voted for somebody other than Mousavi or Ahmedinejad.(1% for reformist candidate Karroubi and 2% for conservative Rezaee).
The 34.4% might include Undecided/Don't know/Refused (knowledge of Farsi would be useful), but even then, this is a suspicious discrepancy that warrants further study.