The World Pool-Billiard Association Tournament Table and Equipment Specifications (November 2001) state: "All balls must be composed of cast phenolic resin plastic and measure 2 ¼ (+.005) inches [5.715 cm (+ .127 mm)] in diameter and weigh 5 ½ to 6 oz [156 to 170 gms]." (Specification 16.)
This means that balls with a diamenter of 2.25 inches cannot have any imperfections (bumps or dents) greater than 0.005 inches. In other words, the bump or dent to diameter ratio cannot exceed 0.005/2.25 = 0.0022222
The Earth's diameter is approximately 12,756.2 kilometres or 12,756,200 metres.
12,756,200 x 0.0022222 = 28,347.111
So, if a billiard ball were enlarged to the size of Earth, the maximum allowable bump (mountain) or dent (trench) would be 28,347 metres.
Earth's highest mountain, Mount Everest, is only 8,848 metres above sea level. Earth's deepest trench, the Mariana Trench, is only about 11 kilometres below sea level.
So if the Earth were scaled down to the size of a billiard ball, all its mountains and trenches would fall well within the WPA's specifications for smoothness.
However, it should be noted that if the Earth were reduced to the size of a billiard ball, it would not conform to the WPA specifications, due to its shape (as well as its composition). The Earth is not a perfect sphere. It is an oblate spheroid. The distance between its poles is shorter than its diameter at the equator by apporoximately 42km. As this is greater than the 28.347km stated above, it would not be deemed sufficiently spherical to pass the test. [Thank you to Neil Brennan for contacting curiouser.co.uk to share this information.]