Does Earth really have two high-tide bulges on opposite sides?
There is no tidal bulge.
This was one of Newton's few mistakes. Newton did get the tidal forcing function correct, but the response to that forcing in the oceans: completely wrong.
Newton's equilibrium theory of the tides with its two tidal bulges is falsified by observation. If this hypothesis was correct, high tide would occur when the Moon is at zenith and at nadir. Most places on the Earth's oceans do have a high tide every 12.421 hours, but whether those high tides occur at zenith and nadir is sheer luck. In most places, there's a predictable offset from the Moon's zenith/nadir and the time of high tide, and that offset is not zero.
One of the most confounding places with regard to the tides is Newton's back yard. If Newton's equilibrium theory was correct, high tide would occur at more or less the same time across the North Sea. That is not what is observed. At any time of day, one can always find a place in the North Sea that is experiencing high tide, and another that is simultaneously experiencing low tide.Read the complete page for more info
(nor fair use to quote the entire article)
Archived here (let's all support archive.org)
While there aren't actually two bulges, many many publications still show it, and teach it.
An example of a University course that teaches there are two bulges
Model of arctic tides
Hudson Strait tides (possibly the largest tides on the planet)
Earth tides and eartquakes
(edit June 27 2015)
Just found this blog post, I like his questions, ones anyone might ask when hearing the old (and wrong) explanation of the two bulges
Here is a 16 day animation from the TOPEX satellite that shows what tides actually look like worldwide.