FrumRav, you mentioned applesauce earlier. The cRc says that “Unflavored, unsweetened applesauce does not need a hechsher.” You can look it up, they sent it out as a Twitter message this past December.
With the vegetables, you left out the part where they listed the exceptions. Again, a quick look at the cRc website will show that they also say frozen vegetables are kosher, with a list of exceptions. The lists don’t sync up exactly, but some research of other hashgachos shows that there are disagreements on the veggies I looked up. A good example is potatoes – the cRc lists them as an exception. Others say they’re fine as long as they’re not fully cooked through.
There are plenty of issues with OO. The kashrus rules of one OO synagogue shouldn’t be your focus.