is there any difference between 'told him' and 'told them' in American accent?

It just depends on how carefully the speaker is talking. People do often fully pronounce “told them” or “told him.” These are definitely different and distinguishable. In formal or public speaking this would be typical. But in some fast casual speech either could become “told ‘em” in which case the two could be the same. 

There are also many Americans who merge those two stressed vowels before nasal consonants (the pin-pen merger). ‘With him’ and ‘with them’ would require careful enunciation to differentiate in these accents.

I definitely heard "told him." So yes, these are pronounced differently: * told him * told them

In general there is usually a difference, maybe a small difference but usually you can tell. Sometimes it is not possible to tell the difference. If they say "told them" as opposed to "told 'em" that's a clear difference and if they say "told 'em" I do expect it to be a wider, more "eh-like-hem" sound and for "him" to be a thinner, more ih/whim sound. In this specific example that's not the case and I totally understand your point. It does sound way more like she's saying "told 'em" as in them than "told him", I only hear it as "told him" because I have the context 

Yes, but some people say told ‘em

Only when you pronounce the “h” in “him” and the “th” in “them.” Told ‘im And Told ‘em Are going to sound very similar and likely indiscernible.

Yes. It can be quite hard to hear, but in that clip she said a sound close to "im," not "em" or "əm," the schwa sound. It's a very small difference. The "d" id usually a little clearer if it's followed by an i, and it was in that clip. So although there is a difference in the way it's said, it's so small that it's very hard for most people to hear, especially in a clip like that or in real life situations with background noise. Some speakers can be even less easy to differentiate than this. I think some people are responding to how they expect "told him" and "told them" to be pronounced, including the h and th, rather than watching the video, which is in a pretty standard accent and casual manner of talking.

"him" and "them" sound very different in an American accent, but both can be verbally shortened to "'em" in some circumstances. she's saying "told him" as "told em." "told them" could also be shortened in the same way.

yes, there'd be a difference since you'll hear a voiced TH with "told them" (told'im vs tol'them). subtle difference too on the last vowel (i vs e). hard to notice since it's not stressed.

The funny thing is that this issue goes back to Chaucer's time. Modern English is mostly based on southern dialects like his. One notable exception is the third person plural pronoun, which was *hem* in southern dialects. Confusion with *him* led us to adopt the northern *them*. The contraction *'em* may partly be a fossil of the southern form, still confusing us.

In my accent, usually, yes. I shorten “them” to *’em* (/əm/ [m̩]) and “him” to *’im* (/ɪm/). “Him” *can* be shortened to a schwa too, but this isn’t common in my accent except in very rapid speech. In this clip, I definitely hear “him” because the vowel sounds unambiguously like /ɪ/ to me, and “them” wouldn’t be shortened to that vowel.

I say told ‘em to which can sorta imply both

they are both often pronounced the same: 'um you can usually switch him to them without issue.

There’s no difference. “Them” can refer to multiple people or just one. “Told him” is more specific and refers to just the one person. Generally you want to lean towards specificity in conversation but it won’t make that much of a difference towards your audience.