County flips in 1900, 1904, and 1908

1908
Parker '04-Taft '08 (anti-trend): 61 in 14 states.

1. Baltimore City, MD (103,423)
2. Suffolk, MA (95,539)
3. Hudson, NJ (85,796)
4. Jefferson, KY (54,700)

Roosevelt '04-Bryan '08: 219 in 24 states.

1. Denver, CO (65,707)
2. Jackson, MO (59,760)
3. Montgomery, OH (42,615)
4. York, PA (30,771)
5. Douglas, NE (30,713)
6. Northampton, PA (23,145)
7. Allen, IN (22,513)
8. Vigo, IN (22,342)
9. Buchanan, MO (18,513)
10. Wyandotte, KS (18,259)
11. Madison, IN (17,204)
12. Lancaster, NE (16,453)
13. Adams, IL (16,314)
14. Pueblo, CO (15,937)
15. Kenton, KY (15,777)
16. Licking, OH (15,166)
17. Tuscarawas, OH (14,205)
18. Allen, OH (13,557)
19. Richland, OH (12,326)
20. Dubuque, IA (11,855)
21. Macoupin, IL (11,664)
22. Boulder, CO (11,629)
23. Darke, OH (11,623)
24. Washington, OH (11,607)
25. Seneca, OH (11,512)
26. Hancock, OH (10,781)
27. Cass, IN (10,344)
28. Wayne, OH (10,084)

Data missing for Texas, but in 1916, only Harris, Dallas, Bexar, and Tarrant Counties cast over 10,000 votes.

Data missing for West Virginia, but none of the turnover counties cast over 10,000 votes in 1912.

1904
McKinley '00-Parker '04 (anti-trend): 87 in 13 states.

1. Baltimore City, MD (97,537)
2. Jefferson, KY (45,959)
3. Baltimore County, MD (17,246)

Bryan '00-Roosevelt '04: 309 30 states.

1. Jackson, MO (48,521)
2. York, PA (28,614)
3. Lehigh, PA (22,358)
4. St Clair, IL (21,561)
5. Northampton, PA (21,557)
6. Allen, IN (20,367)
7. Buchanan, MO (16,859)
8. Jasper, MO (15,537)
9. Adams, IL (14,834)
10. Licking, OH (13,320)
11. Kenton, KY (13,098)
12. Tuscarawas, OH (12,917)
13. Allen, OH (11,603)
14. Richland, OH (11,438)
15. Dubuque, IA (11,353)
16. Darke, OH (10,562)
17. Seneca, OH (10,420)
18. Macoupin, IL (10,272)
19. Boulder, CO (10,172)
20. Cass, IN (10,141)
21. Crawford, KS (10,127)
22. Teller, CO (10,080)

Data missing for Louisiana, Texas, and West Virginia

1900
McKinley '96-Bryan '00 (anti-trend): 110 in 19 states.

1. Manhattan, NY (346,487)
2. Suffolk, MA (91,365)
3. Hudson, NJ (72,627)
4. Queens, NY (28,046)
5. Lehigh, PA (20,517)
6. St Clair, IL (20,063)
7. Adams, IL (17,192)
8. Staten Island, NY (13,201)
9. Dodge, WI (10,778)

Bryan '96-McKinley '00: 332 in 29 states.

1. Salt Lake, UT (26,829)
2. King, WA (18,832)
3. Saginaw, MI (16,769)
4. Wyandotte, KS (15,717)
5. Crawford, PA (15,418)
6. El Paso, CO (14,424)
7. Jackson, MI (12,906)
8. Calhoun, MI (12,413)
9. Pueblo, CO (12,164)
10. Greene, MO (11,864)
11. Bay, MI (11,836)
12. Utah, UT (11,176)
13. Spokane, WA (11,065)
14. Ingham, MI (10,787)
15. Sedgwick, KS (10,719)
16. Pierce, WA (10,589)
17. Sacramento, CA (10,051)

Data missing for Louisiana, Texas, West Virginia

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Obviously, going back before 1920 gets tricky as the data get more incomplete. However, I suspected that in all three of these elections, the anti-trend counties would be disproportionately large.

(There was also, to begin with, a clear, unmistakable national trend in each of these three elections. The swings in 1904 and 1908 were amongst just eleven in history to be over 10%. The swing in 1900 was much slighter, 1.79%, although perhaps more noticeable than it otherwise might be because 1896 was a close election and 1900 clearly wasn't; as Andrew O'Hehir wrote in 2006, 'Bryan came close to being elected president only in his first campaign, the revolutionary autumn of 1896', clearly setting his 1896 bid apart from his other two efforts.)

In each case, the biggest single county to switch was an anti-trend county. (It was Baltimore City twice in a row; the only other time I know of the same one county to have been the largest anti-trend county more than one election in a row is Washtenaw County's run in 1972 and 1976.) In 1904, the first- and third-largest turnover counties were anti-trend counties (despite there being many fewer anti-trend than pro-trend counties), but after that there is a great tendency towards equalisation. Likewise, in 1908, the three largest turnover counties, as well as the sixth-largest, were anti-trend counties, but after that, there is a great tendency towards equalisation. The disproportionality is most evident in 1900 (when there was also by far the smallest swing amongst these three elections). The four largest turnover counties were anti-trend counties (and the largest of them was likely the second-largest county in the country, behind Cook County but ahead of Brooklyn, any county in California [San Francisco was then the state's largest county], and Philadelphia County [and, obviously, Suffolk County, MA]). Beyond that, the sixth-, seventh-, and ninth-largest overall turnover counties were also anti-trend counties. 

In each, case, the pro-trend counties outnumbered the anti-trend counties; in 1900, McKinley flipped 3.018 times as many counties as Bryan; in 1904, TR flipped about 3.55 times as many counties as Parker; and in 1908, Bryan flipped about 3.59 times as many counties as Taft. Interestingly, these ratios all fall short of the norm for elections with clearly anti-trend counties from 1920 on (in which, in general, one nominee flips at least four times as many counties as the other). This may have had something to do with the dynamics of these particular elections, or it may have had to do with the fact that there were fewer counties at the time. The pro-trend counties also, in each case, existed in a significantly larger number of states than the anti-trend counties.