In most countries, exit pollers blanket the country. Your sample is large and if not random, it's so large that the bias has to be either small or glaring.
You get 80% of the polling places and there's only 20% of the remaining to implement the bias.
Exit polling in the US has been mixed. Sometimes it's been really wrong--but we only notice what we want to, so most of the time we didn't notice. In one case in a smaller election, a key precinct had a pollster near the front of the polling place. If you took the bus or walked, she got you; if you drove, you entered through the back, near the parking lot. In another case, the pollster had a long form and a short form, randomly assigned to people--but the people getting the short form sometimes thought they were being told they weren't smart enough for the long form and refused to answer, and that group wasn't randomly distributed between candidates' supporters.
Exit polling in the US relies more on statistics than elsewhere.
Let's say you poll 1000 people and say, "That's going to represent the voting population of California." You pick polling sites in a way to represent the population. Do you pick them all in upscale portions of San Diego, San Fran, and LA? Only in working-class areas? All rural? No, you pick them in various places. Black, white, Latino, upscale and working, urban and rural.
Then when you poll people, you have the pollsters write down demographics: Age (approximate), sex, race/ethnicity, party, all the "intersectional" bits (for the purposes of polling, at least).
Now for problems. What if conservatives don't want to be polled? They walk on out. What if black Democrats look at the old white guy with the clipboard and don't want to interact with him? What if the Vietnamese-speaking pollster can't deal with the surprise 30 voters who don't feel comfortable in English but instead want Korean? You note the people that leave, because they're part of the electorate and you have to backfill in their information ... somehow. You assign them an identity, what's important, and assume that they're part of the mix in a predictable way.
How do you know when your mix matches the population of California that will vote on election day? You made assumptions in picking polling places. You made assumptions about those who don't respond. The assumptions are built on past performance and likely guesses about what'll happen this time. When the raw data comes in, it might be biased as a result of bad assumptions--this election isn't the previous election. So early on you'd report the raw data, because they're so incomplete and you can't do much with it--large portions of the electorate don't vote before 3 p.m. and the raw data at that point are so incomplete as to be of very limited value.
Later, when there are more data, they're fit into a model that you think will match the electorate. You think 15% of the electorate will be black, your pollsters show 20% were black, you weight things according to your model--the data must be biased. Then when polls close and the actual numbers per precinct come in, you find that in fact black precincts underperformed and were no more than 10% of the electorate, so you reweight your data again.
We insist that the raw, biased, unweighted data are right when it suits us. We insist that the initial weighting is right when it suits us. We insist that the final weighting is right when it suits us. But it's all predictive statistics--even the actual exit poll results are still rooted in predictive statistics and are only as good as the assumptions baked into the results--until the final electoral poll results are in. We know the exit poll results have a lot of built-in assumptions, so pollsters conclude that it's more likely their a priori assumptions are wrong than the electoral poll results were.
Predictive statistics come with built-in methods of estimating the size and likelihood of error. When the exit polling is wrong, people cite the margin of error. If the actual error is greater than the estimated error, then that's taken as prima facie evidence of electoral irregularities, fraud, cheating. What estimated error *cannot* account for is error in the assumptions and how measurements are taken. Estimated error is what's built into the methodology, and assumes that the only errors are random, with a truly random data set and accurate measurement.
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