Neptune's first observed orbit
Claim in the list: Since its discovery in 1846, Neptune has completed only one full orbit around the Sun (in 2011).
Verification: Confirmed. Neptune takes about 165 Earth years to orbit the Sun. Discovered in 1846, it reached the first completion point of a full orbit since then in July 2011. This refers to the period since telescopic discovery; the planet, of course, orbited the Sun long before that.
Conclusion: Neptune completed its first full orbit after its 1846 discovery in 2011.