#1 is not really the Efficient Market Hypothesis (EMH). Although there are several forms of the EMH, they all basically say that new information is rapidly incorporated into the price of a security. Thus, all securities are always fairly priced.
I believe market anomalies, specifically non-persistent market anomalies, are what the OP was thinking of. Once these become widely known, they often disappear as arbitrageurs capitalize upon them and force prices to converge.
For example, a famous market anomaly is the January Effect. Historically, stock prices tended to increase more than is warranted in January (this is often attributed to tax-loss selling in December - i.e., investors are selling in December to lock in gains and offsetting losses before the end of the tax year). As this anomaly became more widely know it began to diminish in significance as savvy investors would buy stocks in December only to sell them in January. This resulted in an increase in buying pressure in December (causing prices to increase) and an increase in selling pressure in January (causing prices to decrease). As more and more investors did this, eventually the December prices would increase (and the January prices decrease) to the point where no profits could be made (net of transaction costs). Instead of being able to buy low and sell high, investors would simply be buying middle and selling middle.
To state this simply:
**market anomaly + arbitrage = no market anomaly
I’m not sure if there is a widely accepted name for this, though. “Erosion of market anomalies through arbitrage” explains it, but is not really a name.