Lately I've been bombarded with questions regarding tiny problems too small to consume an entire column space. But that cup now overfloweth, and so, onward.
The unrotatable Remote
Since I upgraded to iOS 7, Apple's Remote app won't rotate. What setting have I got wrong?
I'm afraid the only setting you have wrong is your expectation that it would work in its present form. Apple hasn't yet updated the Remote app to dance entirely in step with iOS 7, so you'll find that regardless of which way you turn your device, no rotation ensues. It's portrait mode, ho! I have to think that Apple will issue an update that fixes this problem shortly.
iCloud-to-Google calendar syncing
The other day you talked about syncing subscribed Google calendars to the Calendar app on your iPhone. Is there a way to do the opposite--sync iCloud calendars to Google?
Unfortunately, no. Apple protects your calendar data (which I believe to be a good thing) by preventing other calendar services from accessing it (which you may not believe to be such a good thing). Thus, no iCloud-to-Google calendar syncing for you (or any of us, for that matter). If calendar sharing is something you need to do routinely, I'd suggest that you rely on Google for that service, as it's accessible to all.
Lost (and found) podcasts
Since upgrading to iOS 7, I've lost the podcasts on my iPhone. What's up?
My colleague Kirk McElhearn dealt with this problem in regard to missing podcasts in iTunes. And his solution has the goods. In your case, however, you're looking for mobile advice.
Launch iTunes and select the Podcasts entry, and you should see all of your podcasts (unless you encounter the problem Kirk addresses). My guess is that those missing from your iPhone will have a gray Subscribe button next to them. Click this button. On your iPhone, launch the Podcasts app and in the My Podcasts screen tap the Refresh button in the top-right corner of the screen. Your missing podcasts should appear.
When read mail isn't
After I updated to iOS 7, the Mail icon in my iPhone's dock started showing over a thousand unread messages. They weren't unread before I updated. How do I remove this bubble from the Mail icon?
Invariably this is a problem with Gmail accounts. Fortunately you have an easy fix. Launch the Web browser on your Mac, travel to your Gmail page, and mark all your messages as read. After you do this, launch Mail on your phone, and allow its message list to refresh; all the messages should be marked as read, and the unread-message count icon should disappear from Mail's icon in the dock.
Now, before you cry, "But I have 10,143 unread messages. Please don't tell me that I have to mark messages in groups of 50!" allow me one further tip.
In your Mac's browser navigate back to your Gmail page and enter is:unread in the mail search field. Just below this field is the Select box (the one with the square and downward-pointing arrow). Click it and choose All. A string of text will appear above your first message that reads 'Select all x conversations in Inbox' (where x is the number of unread messages). Click this link, and you'll select all unread messages, even those that don't appear on the current page. Now click the More box and choose Mark as Read. After cogitating, Gmail will do exactly that. Now, as I explained earlier, return to Mail on your iPhone, refresh your email, and all your messages will be marked as read.