So, I'm going to show my age here, I've been using Mac's since they had little 6 inch green screens and this Yosemite DNS issue the worst Mac problem I've ever encountered. It is even be worse than the dark days of the 7200 series.
I'll start with a positive message to ric_lewis: thank you this helps and clearly does some good.
I'll give you a bit of background. I was running OSX Lion on my Mac Pro and was so frustrated with this OS when I upgraded from (the excellent) Snow Leopard that I couldn't bring myself to even try Mavericks. Eventually the apps I run started demanding Yosemite so I did a clean install (on a new harddrive) and all was well for a fortnight. Then it started.
I'm hard wired into a new Airport Extreme via ethernet but most mornings I can only receive emails (without images) but all my browsers (Safari, Firefox, Chrome) are dead. No connection at all. I found that on the third shutdown and restart the browsers would work. This past week matters have deteriorated further. Within 20 minutes of restarting I lose all browsing capability. Re-boots don't now help, clearing the cache in the browsers doesn't help. I am up and running today as a result of ric's script which I found via my iPad. Incidentally I have to run the script then re-boot my Mac for it to work.
Finally a message to anybody listening from Apple: I've been buying your premium products since the late 1980s. This is the worst issue I've ever seen. How can an organisation of your size and profitability release software that in the year 2015 cannot find the internet? It's embarrassing. I know Yosemite is free, but I'm sure I'm not alone in saying - I'd rather pay for an OS that works than have a free one that falls over. I'm losing 5 hours working time a week on this and I'm starting to think about the benefits of PCs. Please, please, please sort it out.