Left-handed compliment
 

This is a compliment that isn't a compliment at all. In fact it may be a dig. A dig is something said that's meant to hurt. Is there a term for this in Spanish?

un falso cumplido (if it's something subtle)
un agravio disfrazado de cumplido (if it's offensive)

Well, a dig, as I understand it, in Spanish would be something like "un pinchazo". In the sense that Moliner gives for "pinchar", as in, 5 Mortificar, provocar o zaherir. Decirle o hacerle a alguien cosas para que se enfade.

"Zaherir", even if a bit dated, means to "hurt", normally by saying or doing something to humiliate or mortify.

It will be also something like "una pulla".

Moliner gives for "pulla",

pulla1 (del port. pulha) 1 f. Dicho agudo con que se zahiere a alguien. Dicho agudo y gracioso con que se zahiere a alguien en broma. 1 *Broma, burla, chanza, chirigota. 2 Alfilerazo, chafaldita, chilindrina, puntada, puyazo, rehilete, remoque, remoquete, rentoy, vareta.

"Alfilerazo" is one that is used in Spain, as something said that is meant to hurt. Like "pulla".

"Puntada" is similar to "indirecta", in the sense, that just nonchalantly, one says something, to bring up some subject that may be uncomfortable to the listener...

"Soltar una indirecta", is like "to drop a hint", but I believe in Spanish is "stronger" than "just a hint", it could be like the lady who comes to visit Jaimito's mother:

--Jaimito, sé bueno, y no le vayas a decir nada a la madre del bebito que ha nacido sin orejas, que nos viene a visitar...

--No te preocupes, mamá, no diré nada de las orejas.

La visita va bien, y cuando ya están a punto de irse, Jaimito le dice a la nueva madre del bebé sin orejas:

--Bueno, señora, ¡que Santa Lucía le conserve la vista al niño!
--¿Y eso?
--Bueno, es que si no, no habrá forma de sostenerle la gafas...

(Juas-juás)

No es que sea muy fuerte, pero es una ligera "puntada"... (acaban hablando del problema de las orejas, sin mencionarlo...)

Are you sure you don't mean a "Back-handed compliment"? That's an expression widely used in the UK; usually implying 'to damn with faint praise'.

'Your hair's a bit nicer than it was', 'the team played a bit than they have been doing', that sort of thing.

Your can use both left handed and back handed compliment in the United States. They both mean an insult disguised as a compliment.