The adjusted price reference you made is axiomatic. Adjusted prices simply subtract the dividend. It does not reflect market value. You'll notice the open on the day after the dividend, the stock actually went up $0.40 from the closing price.
When shorting, you only pass the dividends through. The company sends you the dividend, you send it to the original owner, you could still profit from the drop in share price.
Well, the stock price might have changed because of some news or general market sentiment. I guess I could have found a better example, a stock where the dividend is much bigger (percentage-wise), the effect would be much clearer then.
No, shorting doesn't work that way, obviously. "Shorting" means you sell he stock, so the new owner gets the dividend, not you. That's one reason shorting equities is very risky long-term.
The ex-dividend date is an implementation flaw that makes the stock price discontinuous at the dividend date (I initially misunderstood this). However, in theory, a pro-rata dividend would be continuous.
They do. But you don't usually see this, because the prices are "adjusted", to make price history continuous, same as with stock splits.
Take a look at MSFT (Microsoft) stock price on Yahoo! Finance. "Close" is what actually happened, and "Adj Close" is what you see on the graph.
https://uk.finance.yahoo.com/q/hp?s=MSFT> investors could simply short the stock and get a guaranteed profit
No, to short a stock you need to borrow it first. If you borrow a stock, you owe the dividends that were due in the meantime.