This evening, my six-year-old daughter remarked of her sister, "Mommy, Kyla's four and she still can't say 'th'. She can't say the word 'thing' right."
As we tried unsuccessfully to get her to say it correctly, I had some interesting insights about the way people mispronounce the "th" sound. There are actually two versions of it, the voiced (as in that, this, the) and the unvoiced (thing, theory). Kyla mispronounces both of them, but she preserves the voiced/unvoiced character when she does: "Dat's de fing." The voiced "th" is replaced by "d", which is also voiced; the unvoiced "th" is replaced by "f", which is unvoiced.
My Taiwanese parents also have difficulty with the "th" sound, but they have different voiced/unvoiced substitutions: "Tzahs tze sing." My Russian violin teacher substitutes a voiced "z" and an unvoiced "t": "Zat's ze ting." Although I haven't yet done an exhaustive study, I suspect that all foreign accents that replace the "th" sounds do so in a way that preserve the voiced or unvoiced aspects as appropriate.
It seems to me that this kind of voice-aspect-preserving substitution makes up a huge fraction of the consonant differences we perceive in foreign accents. A native English speaker trying to speak Spanish will frequently confuse the voiced "b" and "v", (haber and a ver are actually homonyms) or the "d" and voiced "th" (todo is generally pronounced more like to-tho).
I wonder if I could predict how a native speaker of a given language would pronounce English without ever meeting one, simply by studying the voiced and unvoiced sounds that exist in that language.