Well, Levofloxacin has some neurotoxic effects of its own.

The family it belongs to, all share this characteristic.
Here is a monograph with more information:
http://www.drugs.com/ppa/levofloxacin.html

This drug can cause neuropathy. If you Google it with the
keywords--- Levofloxacin neuropathy--- you will see various
reports.

This antibiotic can disrupt the GI flora and cause diarrhea.
In patients who use other antibiotics often, this may lead to
infection with C. difficle, or other forms of colitis. (diarrhea)
This may need special treatment and should be evaluated by a doctor.

Levofloxacin prolongs QT interval of the heart, and therefore can be additive to other drugs, be dangerous if you are dehydrated and low in potassium and magnesium, or have a genetic tendency for this. There are isolated reports of MDMA affecting the heart, but not much else is available that I can find now.
Levaquin itself is a major drug and has potential for causing long term reactions. One of these is tendon ruptures, which may occur up to a year after use of this drug.
Some people have visited on this forum after one course of this antibiotic with neuropathy as a side effect.

CNS effects are also possible, but depend on age and dose.
Elderly taking high dose may develop confusion, seizures and other CNS effects. This is less likely in younger patients.
This drug can damage the liver and in fact two other fluoroquinolones have been taken off the market in the US for this. In fact Floxin oral has fallen also into disuse because of seizures it caused. The book Bitter Pills deals with it.
http://www.stephenfried.com/bitter-pills/

This site discusses the side effects of fluroquinolones from a medical perspective:
http://www.medicationsense.com/artic...cs_052205.html