When a Spanish speaking person rolls their Rs unnecessarily in English, I think most of us native English speakers just perceive it as an exotic characteristic of speech -- not some kind of impairment. However, when a native Chinese speaker pronounces an L more like an R, it generally sounds more like a speech impairment.

My guess is that when we don't trill the consonants in the same way as native Spanish, Italian, or Russian speakers do, then it sounds more like an impairment than an exotic trait carried over from a different tongue. Can any native speakers of languages with trilled consonants comment on this? Do we sound dumb?

BradP:When a Spanish speaking person rolls their Rs unnecessarily in English, I think most of us native English speakers just perceive it as an exotic characteristic of speech -- not some kind of impairment. However, when a native Chinese speaker pronounces an L more like an R, it generally sounds more like a speech impairment.

To Koreans and Japanese, the English R sounds like some nondescript vowel. It's very similar to the Mandarin R, so the Chinese do not perceive this as an "impairment."

By the way, although the Japanese have trouble pronouncing L, the Chinese do not. They have an L sound in their language as well as a retroflex R sound. Koreans have both L and R sounds but regard them as allophones of the same phoneme, so they may confuse them in certain contexts.

A Frenchman once told me that when English speakers speak French using the English R, they sound like they're trying to talk with a mouthful of potatoes.

Those with a trilled alveolar R would probably feel the same way hearing an English speaker speak their language with the English R, that an English person would feel hearing a Danish person speak English with a Danish R.

The Danish R is as if they took the guttural R and the alveolar R and decided they couldn't choose, thus they use a consonant that's actually more a vowel (a deep a/o sound).

RE Chinese, I think (for Mandarin speakers at least, others don't count as much due to some languages/dialects lacking that R) seems like the R is strange because when you hear it, it doesn't "match" the rest of their accent. They tend to pronounce each syllable very clearly, but have a retroflex R, where as those English speakers with a retroflex R don't pronounce their syllables as clearly.

E.g. (right)
Chinese person "rait"
Some random American person with retroflex "rah'"
etc (that's not a scientific comparison, but that's the reason we still perceive a Chinese accent and R as "different" in a nutshell)

Do you mean when a Spanish or Italian speaker hears a native English speaker speaking Spanish/Italian, or English, or Esperanto, or what?

I don't know about Italian (I don't speak it) but I know that in Spanish there's a difference between a rolled R and a single (unrolled) R. The word for pear has a single R, but if you roll it, it becomes the word for a female canine. It's a minimal pair, like Z/S in English. (If you're going to sue, that's different than if you're going to the zoo, but you could always sue the zoo with Sue to cover all your bases.)
Anyway, so if you don't roll your Rs appropriately in Spanish, it's just like when you hear someone speaking English who can't differentiate between Y and J (yellow/jello.) It sounds foreign and may be a cause for some giggles.
Most English-speakers, when speaking Spanish, have a tendency to make the R sound when they should make the D sound.
Sorry, I'm rambling.