Because elements are classified by the number of protons they have, could there potentially be planets or environments that are so dense that they are made up of elements potentially greater than Ununoctium? Although, it would most likely be ridiculously unstable, the properties of all these new elements and their effects leaves me in curiosity.
Planets, in the terrestrial ball of rock sense, won't be comprised of elements past ununoctium, because those elements aren't formed in supernovas, which are what create the majority of the terrestrial elements that form rocky planets. Furthermore, planets don't have enough gravity to hold together larger balls of nucleons through gravity alone.
However, there are objects that do. They're called neutron stars. In neutron stars, intense gravitational forces can stabilize nuclei of substantially greater size than what are found in 'ordinary' matter. Furthermore, the core of a neutron star is of such density that it can, in some ways, be thought of as a single giant nucleus. Unfortunately, most of the heavy nuclei found in neutron stars are expected to have far more neutrons than protons, so it's hard to say exactly what the largest atoms found in a neutron star are in terms of atomic number. Nonetheless, neutron stars are probably the closest thing to a ball made of huge atoms you can find in the universe.
"But wait!" you say, "Those are stars, not planets!" Well, as luck would have it, the new IAU definition of a planet doesn't specify any limits on the composition of a planet, merely on its size. Theoretically, there's no reason a neutron star can't be small, though the circumstances which create them tend to lead to stars with masses a few times that of our sun. If a neutron star were to somehow lose most of its mass during formation and pop out with a mass lower than around 13 Jupiters, and was then captured in orbit around a star, whereupon it would presumably clear its orbit, you would have a planet comprised mostly of huge atoms.
Most of the elements theorized to exist at those high numbers are extremely unstable and tend to break down quickly. According to Wiki, all elements over 101 (except dubnium-268) have a half-life less than a day. So unless we discover the 'Island of Stability' (and it is significantly more stable than expected) theorized most of the elements would deteriorate before a planet could even be formed.
It would however suggest that the planet was created by an intelligence should one exist, though why?
I'm no nuclear physicist, but I'll take a crack at this. As you stated ununoctonium and the like are extremely unstable. If a planet of ununoctonium appeared it would decay in milliseconds. The only way I could see this happening is if your planet was constantly bombarded with enough energy to continually form new heavy elements. Cosmic ray spallation is known to produce heavier radioactive isotopes (cosmogenic radioisotopes), compared to normal stellar nucleosynthesis. A casual search brought up the idea of a planet bombarded by a ultra-high-energy cosmic ray. A source of these rays, called a Zevatron (I love science words), could be a relativistic jet from an active galactic nucleus. One example of such a jet is in the M87 galaxy, the energy of which has been estimated at 5.1 × 1049J
So basically, a planet directly over the center of a supermassive black hole in a center of the galaxy might be bombarded with enough energy to produce some heavier elements. Or far more likely just disintegrate.