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[1]

K.A. Bush, Classroom Notes: On an Application of the Mean Value Theorem. Amer. Math. Monthly 62 (1955), 577--578.

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M.R. Spiegel, Mean Value Theorems and Taylor Series. Math. Mag. 29 (1956), 263--266.

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D. Zeitlin, Classroom Notes: An Application of the Mean Value Theorem. Amer. Math. Monthly 64 (1957), 427.

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C.L. Wang, Classroom Notes: Proof of the Mean Value Theorem. Amer. Math. Monthly 65 (1958), 362--364.

(In this article, the derivation of MVT from Rolle's theorem by tilting one's head is presented in horrible analytic detail.)

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J.P. Evans, Classroom Notes: Sequences Generated by Use of the Mean Value Theorem. Amer. Math. Monthly 68 (1961), 365.

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L.C. Barrett, Classroom Notes: Methods of Proving Mean Value Theorems. Amer. Math. Monthly 69 (1962), 50--52.

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L.W. Cohen, On being mean to the Mean Value Theorem. American Mathematical Amer. Math. Monthly 74 (1967), 581-582.

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L. Bers, On avoiding the Mean Value Theorem. American Mathematical Amer. Math. Monthly 74 (1967), 583.

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H. Levi, Classroom Notes: Integration, Anti-Differentiation and a Converse to the Mean Value Theorem. Amer. Math. Monthly 74 (1967), 585--586.

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R.P. Boas Jr., Classroom Notes: Lhospital's Rule Without Mean-Value Theorems. Amer. Math. Monthly 76 (1969), 1051--1053.

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D.E. Sanderson, Classroom Notes: A Versatile Vector Mean Value Theorem. Amer. Math. Monthly 79 (1972), 381--383.

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R.P. Boas Jr., Who needs these mean-value theorems anyway? Two-Year College Math. J. 12 (1981), 178--181.

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T.W. Tucker, Rethinking Rigor in Calculus: The Role of the Mean Value Theorem. American Mathematical Amer. Math. Monthly 104 (1997), 231--240.

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H. Swann, Commentary on Rethinking Rigor in Calculus: The Role of the Mean Value Theorem. American Mathematical Amer. Math. Monthly 104 (1997), 241--245.

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J.J. Koliha, Mean, Meaner, and the Meanest Mean Value Theorem. American Mathematical Amer. Math. Monthly 116 (2009), 356--361.

This represents less than 10% of list was compiled as follows: first I started with the available literaturefive or so articles on MVT that I remembered, mostly from having appeared in the Monthly. Then I believedid a MathSciNet search: "Anywhere=(mean value theorem)". If you want to add references, please feel freeThis gives 1589 matches. (Note that they are ordered chronologically rather than alphabetically.) If you would like to supplement the references Starting with free links to the actual earliest papers, I looked quickly through the articles until I got tired. My list contains all the articles that would I spotted and thought to be fantasticof relevance to the question which were published before 1973. This was about 25% of the 1589 matches.
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The purpose of this answer (which I would make CW even if the question weren't) is to collect references to scholarly articles on MVT and its role in introductory calculus courses. Most of these articles have some real mathematical content: e.g. they discuss logical implications between different forms of MVT. Certainly they are written by people who have thought deeply and in novel ways about this result -- i.e., by mathematicians.

[1] L.W. Cohen, On being mean to the Mean Value Theorem. American Mathematical Monthly 74 (1967), 581-582.

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[2] L. Bers, On avoiding the Mean Value Theorem. American Mathematical Monthly 74 (1967), 583.

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[3] R.P. Boas Who needs these mean-value theorems anyway? Two-Year College Math. J. 12 (1981), 178--181.

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[4] T.W. Tucker, Rethinking Rigor in Calculus: The Role of the Mean Value Theorem. American Mathematical Monthly 104 (1997), 231--240.

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[5] H. Swann, Commentary on Rethinking Rigor in Calculus: The Role of the Mean Value Theorem. American Mathematical Monthly 104 (1997), 241--245.

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[6] J.J. Koliha, Mean, Meaner, and the Meanest Mean Value Theorem. American Mathematical Monthly 116 (2009), 356--361.

This represents less than 10% of the available literature, I believe. If you want to add references, please feel free. (Note that they are ordered chronologically rather than alphabetically.) If you would like to supplement the references with free links to the actual papers, that would be fantastic.