If attacking a Targaryen physically was punishable by getting a hand lopped off, what are the various punishments for slandering them? What legal ramification would be imposed on the various Lord/Lady who dared to talk shit? ((And got caught?))

It very much depends on status:

“One more thing. A trifling matter.” He gave her an apologetic smile and told her of a puppet show that had recently become popular amongst the city’s smallfolk; a puppet show wherein the kingdom of the beasts was ruled by a pride of haughty lions. “The puppet lions grow greedy and arrogant as this treasonous tale proceeds, until they begin to devour their own subjects. When the noble stag makes objection, the lions devour him as well, and roar that it is their right as the mightiest of beasts.”

“And is that the end of it?” Cersei asked, amused. Looked at in the right light, it could be seen as a salutary lesson.

“No, Your Grace. At the end a dragon hatches from an egg and devours all of the lions.”

The ending took the puppet show from simple insolence to treason. “Witless fools. Only cretins would hazard their heads upon a wooden dragon.” She considered a moment. “Send some of your whisperers to these shows and make note of who attends. If any of them should be men of note, I would know their names.”

“What will be done with them, if I may be so bold?”

“Any men of substance shall be fined. Half their worth should be sufficient to teach them a sharp lesson and refill our coffers, without quite ruining them. Those too poor to pay can lose an eye, for watching treason. For the puppeteers, the axe.”

“There are four. Perhaps Your Grace might allow me two of them for mine own purposes. A woman would be especially …”