Hi Skydiver, 🙂
1. I do not think the episodes themselves are in flash, because the video "clips" that CBS offers on the site are viewable on my iPad. I believe the commercials added in are tacked on in flash.
The reason I believe it is specific to the advertisements is that I have this same experience with youtube videos. I am able to view most youtube videos in Safari on my iPad by setting my iPad's Safari to mobile youtube settings. The only time I have a problem is if the youtube video has a Flash ad in front of it. Then I get redirected to the iPad's youtube app. My experience is that it isn't the video; it is the advertisement. Youtube has control of these advertisements that are placed in front of their videos.
Also, as previously mentioned, I can view the other video clips on my iPad on the CBS.com Big Brother page just fine. It is only the ones that they have added advertisements to that do not appear on my iPad.
The problem seems specific to the advertisements, which seem Flash-oriented.
2. I have not found this CBS app you are referring to. I checked the iTunes store for CBS apps and did not find one that plays prime time television shows. Searching for CBS apps brings up "CBS News," "CBS Sports," "CBS This Morning," "CBS Sports Pro Football," "CNet," "60 Minutes for iPad," but not just a plain vanilla CBS app as you suggested that would allow me to view CBS prime time television programming on the iPad. A plain CBS app does not exist at the moment, although it may have in the past.
I also viewed iPhone apps hoping they would make one that I could use on the iPad, but only one possible choice there: a third-party app called TV.com. It is not made for the iPad, so it is not iPad native. So no full screen viewing (my point of having an iPad and viewing videos is to watch them full screen).
I downloaded the TV.com app and tested it. They did not have the latest Big Brother episode from last night, Episode 19. That episode has been on the CBS.com website as of last night (I watched it on my MacBook.) They have the typical 1x and 2x viewing options of iPhone apps. The video quality is "okay" but not great. I could only test it with Episode 18, an older ep, as Episode 19 is entirely missing from that app.
3. I am aware of the browsers that you mentioned, but I have no experience with them, either. 😉 Puffin has a free version with a two-week trial. Once the two weeks expires, you have to upgrade to the full version in order to retain functionality. Looking at some reviewer's comments, although it handles Flash, it seems there may be a problem using a keyboard with it, and someone else mentioned a problem using Airplay to push it to an Apple TV. Others complained about speed issues, even though they have fast internet connections. Also the update seems to have made Puffin's sound disappear. Bottom line, I do not know if the devs of these third-party browsers are as on top of their game and their upgrades as Apple is with their upgrades.
If only the site developers for CBS and other sites would go ahead and switch to the html5 format so that this becomes a moot discussion.
4. I have looked for Big Brother apps, but most are focused on providing stats/notifications on what is happening inside the Big Brother house, so no luck there.
5. I have to disagree with you: 🙂 CBS does have Big Brother listed in my On Demand cable listings. They have the last 11 full episodes listed, including the episode from last night. In addition to Big Brother, CBS lists Big Bang Theory (4), Blue Bloods (3), CSI (4), CSI NY (2), Hawaii Five-0 (3), NCIS (4), NCIS:LA (4), The Good Wife (2), Two and a Half Men (5), Undercover Boss (2). The number in parentheses is the number of shows available On Demand. That's 11 shows. Not all of their shows, but frankly, not much is showing on CBS right now in this gap between summer and fall television. Fox is showing 19 shows On Demand, but these include shows that are not currently running such as Bones, Glee, and New Girl. NBC is showing 10 shows On Demand so is showing less shows than CBS, and this includes Grimm, and some others which don't have seasons currently running right now.