JD350 straight
1965 10001 - 16183
1966 16184 - 42484
1967 42485 - 64992
1968 64993 - 88280
1969 88281 - 102136
1970 102137 - 117499
JD350B
1970 117500 - 121137
1971 121138 - 138708
1972 138709 - 164035
1973 164036 - 191172
1974 191173 - 219507
1975 219508 - ?
The main differences between the JD350B and JD350C are that the C went to a 3/164 CID engine from the 3/152 CID in the JD350B and that the JD350C changed from dry to wet steering clutches.
JD350C
1975 219500 - 240367
1976 240367 - 261203
1977 261204 - 287209
1978 287210 - 313955
1979 313956 - 340929
1980 340930 - 365413
1981 365414 - 378065
1982 378066 - 383599
1983 383600 - 388915
1984 388916 - 393400
1985 393401 - End
Sometime during 1985, the serial number scheme was changed and the new range started in the 700000 range. So, there are some 350C units showing serial numbers in the 700000 range prior to number 723603. However, we do not know the beginning serial number in this new range.
JD350D
1985 723603 - 726752
1986 726753 - 732791
1987 732792 - 742866
1988 742866 - End
The source of the data is from a farm equipment quick reference guide that's intended to assist dealers in determining the year and current market value of trade-in equipment.
The guide as such only lists the beginning serial number for each year. I'm making the reasonable presumption that the last serial number for any given year is one less than the starting serial number for the successive year.
Thanks to Digitup for sharing the relevent pages from his guide with us so we can determine what year a given machine is.

Stan
Additionally, some model numbers contain an extra letter. At some point during the manufacturing of the 350B, they added a letter. Making the model one letter longer. Such as 350BE.
A - Diesel, Loader
B - Diesel, Loader
E - Diesel, Inside Dozer
G - Outside Dozer
J - Drawbar Crawler
W - Wide Track
The meaning of the letters csme from the JD350C manual section 1A3. There was no data on what the difference is between the A and B loaders.
Stan