I'm going to skip the first two items ("You have to get the baby circumcised because it is really hard to keep a baby's penis clean" and "Little boys won't clean under their foreskins and will get infections"), because as presented they're so extreme that they almost are myths. That said, it is easier to keep a circumcised penis clean (except for the brief healing period, of course), and uncircumcised penises are more prone to infections.
Myth: Uncircumcised penises get smelly smegma. Reality check: Actually, smegma is produced by the genitals of both women and men during the reproductive years. Smegma is made of sebum and skin cells and lubricates the foreskin and glans in men, and the clitoral hood and inner labia in women. It is rinsed off during normal bathing and does not cause cancer or any other health problems.
Actually, these are rather dubious statements. A few hypotheses have been proposed, but to date no evidence supports the notion that smegma has any biological function. What little evidence there is suggests that it is associated with penile inflammation, HIV, and with penile cancer. (I should note that this evidence isn't particularly strong.) In the case of penile cancer, for example, all three of the human studies to investigate found an association between smegma and penile cancer; see here.
Myth: "My uncle wasn't circumcised and he kept getting infections and had to be circumcised as an adult." Reality check: Medical advice may have promoted infection in uncircumcised males. A shocking number of doctors are uneducated about the normal development of the foreskin, and they (incorrectly) tell parents that they have to retract the baby's foreskin and wash inside it at every diaper change. [...]
The author elaborates further on this interesting hypothesis, but utterly fails to provide any evidence whatsoever. But there's a really simple way to test it. If the difference is due to lack of knowledge about the foreskin in countries with high prevalence of circumcision, then we'd expect that studies conducted in countries with low circumcision rates wouldn't see any difference. In fact, though, the difference is observed both in the US and Canada (both of which have relatively high percentages of circumcised men) and in the UK and New Zealand (both of which have relatively low percentages of circumcised men).
Myth: My son was diagnosed with phimosis and so had to be circumcised. Reality check: Phimosis means that the foreskin will not retract. Since children's foreskins are naturally not retractable, it is impossible to diagnose phimosis in a child. Any such diagnoses in infants are based on misinformation, and are often made in order to secure insurance coverage of circumcision in states in which routine infant circumcision is no longer covered.
While an interesting conspiracy theory, there's no evidence for this. Phimosis can be diagnosed at any age, partly because acquired phimosis tends to be characterised by the presence of whitish, hard scar tissue at the tip of the foreskin. It may be overdiagnosed in children, but to claim that it cannot be diagnosed is dangerously misinformed.
Myth: Uncircumcised boys get more urinary tract infections (UTIs.) Reality check: This claim is based on one study that looked at charts of babies born in one hospital (Wiswell 1985).
Wrong. There have been about 25 studies to date. See here for a partial list.
Myth: Circumcision prevents HIV/AIDS. Reality check: Three studies in Africa several years ago that claimed that circumcision prevented AIDS and that circumcision was as effective as a 60% effective vaccine (Auvert 2005, 2006). These studies had many flaws, including that they were stopped before all the results came in. There have also been several studies that show that circumcision does not prevent HIV (Connolly 2008).
Here the author is mistakenly treating all studies as equal. They aren't. The most rigorous studies are of a type called randomised controlled trials. The most important characteristic of these studies is that circumcision is performed as part of the study, and men are selected to be circumcised at random. A less rigorous (but much cheaper) study design is to look at men who've been circumcised previously, and see whether they're HIV positive or not. This design is called an observational study, and the main problem with it is that circumcision is often associated with something else (say, religion) that's also associated with behavioural differences. So it's difficult to tell whether circumcision, or these behavioural differences, are responsible.
Of about 50 or so observational studies to date, probably 40 have found a protective effect. All three randomised controlled trials did likewise.