Yep. There are glitches in Silver, quite a lot of them actually.
According to Bulbapedia, there are nine glitches known to them in the second generation.
Here is a list of second generation glitches:
• Celebi egg glitch (only by hacking the game, but you use a glitch egg that knows the move Beat Up, than follow a series of steps to obtain a Celebi, which is currently the only way to obtain Celebi)
• Coin Case glitches (which involves a coin case glitch and Pokemon cries)
• Error codes (a series of codes that appear when the game is not functioning properly)
• Infinite continues glitch (note that this is not in Silver)
• Johto guard glitch (a glitch that allows players to trade Generation II Pokemon to a Generation I game)
• Mail delivery glitch (a glitch that allows a player to have one or more unhatched glitch eggs in their party)
• Sketch glitch (a glitch where you could use the move Sketch and keep the Sketched move at the end of the battle, which was used to be exploited with Smeargles and sketched whatever desired moves in the Trainer House.)
• Teru-sama (a glitch item in all Generation II games that serve nearly no purpose but can be sold for 19660 Pokedollars)
• Trainer House glitch (a glitch that affects the trainers in the Trainer House where if you set the time right after a trade or Mystery Gift, it will cause you to fight a trainer called PKMN Trainer Thomas that is displayed as 9's, and sends out Lv 0 Pokemon, which shows the same sprite as the trainer, and freezes the game immediately)
If you'd like a more detailed explanation of each glitch, simply click the links of the name of the glitch, which will re-direct you to Bulbapedia, along with more information on each glitch.
Have fun! ~