In most North American English dialects, the pronunciation of the /o:/ is less diphthongized than elsewhere, which makes it significantly closer to a pure long “o” than in Received pronunciation. Because of this, when the tongue moves toward the front of the mouth in order to articulate the “th” at the end of “both”, it passes very close to where a postvocalic /l/ would normally be articulated. Depending on the individual or the dialect, an “l” sound can sometimes be heard.
This is also commonly mispronounced by children who are 8 years or younger. Between ages 5 and 8, /l/ and /th/ are the fourth and third last phenomes to be mastered completely and are often switched around.
In both modern British and American English, it is fairly common to pronounce the interjection “well” as “wool,” “woll,” or “wull”. Certain dialects and accents can emphasize this sound more.
This is an example of the neutralization of the phonetic /ɛ/ sound that sometimes occurs when speaking quickly or with loose lips. That is to say /wɛl/ becomes /wḷ/ or even /wʊ/, most often when preceding a vowel phoneme, such as in “yeah” or “alright”.
Such a linguistic combination represents a bilabial to voiced alveolar lateral approximant to postalveolar shift. In other words, moving your tongue from the front of your mouth, just below the teeth, to the roof of your mouth, to scrunching it up in the back, all without closing your lips. This transition is fairly complex, and sometimes the mouth will take a shortcut by not extending its corners as much. This, finally, can result in a slight /ʊ/ or “oo” sound.