My experience was bloody awful, but most of it's already been covered here. To add:
Death-wish farmers bolting around single track country lanes on tractors at 30-40mph - they don't care if oncoming traffic can't see them, if it's foggy or pissing down with rain
Local roads being chewed up by heavy machinery and not repaired
Really aggressive farm dogs
Building works happening when it suits them - til it's dark, all weekend, Christmas Eve, etc
I think a great deal depends on what sort of farmers you end up living next to. There are considerate farmers and there are DGAS farmers.
Someone mentioned shooting parties. Outside our lounge window at 8am on a Sunday. Then members helping themselves to our garden/drive to fetch dead prey.
When people talk about flies (we were on a dairy farm), for us, that was for 11 months of the year, and if you're unlucky, they'll be coming up through the pipework, through extractor fans, out of the dishwasher, crawling through gaps in windows. I cannot emphasise enough how awful life is when you cannot keep the fuckers off you or food that you are making. It was impossible to operate in our house without a series of fly nets, and I remember one particular occasion I had to get my partner to stand next to me whilst I made sandwiches to swat away flies. It didn't work, one of the fuckers still got on the bread. I live on a river now and we get a pretty high level of creepy crawlies and flying things, but they don't have a patch on how rage-inducing farm flies are. I imagine they'll be lower in number on a farm with no animals.
Except to ask - do you know they don't rent any of those fields out at certain times of the year for lambs? Because some do.