Read about them here:
Some of these alleged anachronisms can be written off as narrative flourishes from Tolkien as the 'translator' of the Red Book of Westmarch. We don't have to imagine Bilbo himself writing of express trains or telescopes. And Smaug's waistcoat is merely a metaphor.
YES! The Fox is mentioned!
-Sorry I had to :)
Thorin also mentions in the fight between the mountain giants that they might be kicked sky high for a football.
Good catch, but it may not have been that much of an anachronism, since football (aka soccer in some countries) has been played in some form since the 12th century.
I have noticed that Hobbiton seems to be a few centuries ahead of places like Gondor and Rohan, at least in household luxuries. Maybe it's because they never wasted resources on an army and thus became technologically advanced in home life.
My guess is that Bilbo's mantle clock was of Dwarf-make, maybe a gift from his father to his mother.
Technically, "lamp-like eyes" makes some sense, as lamps weren't the lightbulb ones we use today. They have the same name but they were candles in traylike carriers with handles.
Oil lamps have also been in existence for thousands of years. And don't forget that even before the Two Trees of Arda existed Arda was lit by the Two Lamps