These 13 astrological signs are
- Scorpio (constellation: Scorpius)
In between the sun passing through Scorpius and Sagittarius, it spends a while in Ophiuchus. In fact, the Sun spends more time in Oph than it does in Sco, begging the question of whether the Sun spends the exact same amount of time in each other sign, as is implied by the fact that the dates for signs are evenly distributed. If what matters is where the Sun is in the sky, it should matter how long it spends in each sign.
Note in the image to the right the red dashed line representing the ecliptic (the Sun's path), the yellow dashed lines indicating constellation borders, "Sgr" (Sagittarius) in gray on the left, and the little sliver of "Sco" (Scorpius) passed through on the right on the Sun's way from "Lib" (Libra).
As for Ophiuchus, it is one of the 88 internationally recognized constellations. The exact borders were proposed in 1875, and accepted by the International Astronomical Union (IAU) in 1933, but the thing to keep in mind is that they had been used in common practice for centuries earlier. Millenia even: the first record of any information about the constellations dates to the 700s BCE. (And unlike the IAU's decision on Pluto, the definition of constellations appears to have been entirely uncontrovertial and unchallenged.)
So two flaws to astrology: Ophiuchus isn't included, and each of the 12 (incorrect) signs is given the same amount of time, even though the Sun spends a different amount of time in them.