Bloomberg tracked poll results on the Brexit vote. The final value before the election (on June 22nd, 2016) was Remain 46.2% Leave 44.3% with 9.6% undecided (doesn't add to 100% due to rounding). That's a 1.9% margin, well within the margin of error. The actual election was 3.78% in favor of leaving. That's a 5.7% swing. That's large but not unheard of.
Every day leading up to that last polling result, from June 12th to June 21st, Leave was ahead. On June 15th, 3.8% ahead. Then the polling switched back. But in the actual referendum, the result was closer to the June 15th polling result. Maybe it would make more sense to regard the June 22nd polling result as the outlier. Most of the data was pointing the other way.
Another issue is the relatively large undecided contingent. Note that both Remain and Leave outperformed their nominal results in the poll. Did undecideds break towards Leave?
Historical presidential polling
Some examples from that data:
US presidential polling 1992
In 1992, the final presidential poll result was +12% Clinton. The actual result was +6% Clinton. Both Clinton and Perot showed significantly different results in the actual election. So presidential polling in 1992 was no more accurate than Brexit polling in 2016.
Did the October surprise revelations about a Caspar Weinburger prosecution change things? If so, it's hard to see in the polling, as Bush was essentially flat. It was Clinton's polling that fell.
US presidential polling 1988
Think that 1992 was an exceptionally odd election? Possibly, but in 1988, polling was also off by 5%. Bush had a 12% lead in the last poll but only finished 7% ahead in the actual result.
US presidential polling 1980
In 1984, polling was quite consistent with the final result, but in 1980, we had a 7% swing from Carter to Reagan.
US presidential polling 1976
Only a 3% swing, but from a small lead by Ford to an actual win by Carter. The polls were wrong!
US presidential polling 1964
In polling, Johnson had an 18% lead, but in the election, he only won by 13%. Another 5% swing. Especially relevant in this election with the replay of the Daisy ad. Will that hurt or help Trump?
US presidential polling 1952
A slim 2% lead turned into an 11% blowout for Eisenhower. That's a 9% error.
US presidential polling
I'll leave it up to you to decide whether this is accurate or not accurate. But in US presidential polling terms, the Brexit result would not have been uncommon. The uncommon part is that it crossed the line for victory, not the actual difference between the polled result and the actual result.
Absent additional revelations, neither candidate will win a double digit victory. Clinton's +2.8 in the Real Clear Politics average suggests that she has a slightly better chance of doing so. But that could change, as the polls are much tighter this week than last.
Note that the 538 average has Clinton doing better: 49.4% to 44.3%. The 538 average weights polls with greater historical accuracy more highly. That may or may not prove to be accurate. It's worked well in recent elections, but there haven't been enough data points to really evaluate it.
There will be much speculation about the impact of the Comey letter to Congress. There will be little actual evidence of impact though, as the polls were already in motion. Is the additional motion because of the letter? Or previous information sinking into the results? Or random chance? No one will actually be able to tell, but many will opine.
The national popular vote result doesn't actually matter. What's important is the state-by-state results. There is less information there though. And the polling averages can be slow to update.