“What are some side effects of local anesthetics?”

The initial injection of local anesthetics may be somewhat painful, depending on the speed of injection (faster injection is more painful) and specific local anesthetic used (bupivacaine is more painful than lidocaine). Local anesthetics do not work instantly, so it is important to
wait after local anesthetic injection before doing any skin incision. Excessive amounts of local anesthetic, if given intravenously, can produce ringing in the ears, perioral numbness, or even seizures. Finally, all local anesthetic-induced numbness eventually wears off, so it is important to have pain medication prescribed to take as the numbing recedes.

Really not much of any side efffect

When used appropriately Local Anesthetics are very safe and effective tools for surgical procedures. These two groups of LA, esters and amines. Some patients could be allergic to others, such as Procaine. The most dangerous complication of LA could be LAST, or local anesthetic systemic toxicity, when too much of LA is administered, or it’s injected into blood vessels instead of surrounding wound tissues. It’s a rare but potentially fatal complication usually avoided with proper technique and proper total dose per Patients weight. Also treatable when in a timely recognized. Extremely rare. Some LA such as Prilocaine in high doses could cause Methemoglobinemia, and affect red blood cell's Oxygen caring capacity. Again avoidable and treatable condition. In general, LA is safe and successfully used for ages.

Please use YOU Tube and Wikipedia for detailed explanation.

Allergy/ anaphylactic reaction
dizziness, headaches, blurred vision, twitching muscles, continuing numbness, weakness or pins and needles.
finding it hard to pee or leaking pee (epidural)
Local anesthetic toxicity which includes Seizure and heart block