Is there an extra yud in our Torah in parshat Devarim, according to Rashi?

It is certainly possible. Anan Lo Bekiin in malei vs. chaser. And IIRC, we see arguments in masoretic seforim about this all the time. The difference here is that Rashi notes that a word is written chaser, and darshens it, whereas we do not have this textual feature. In which case his sefer Torah is different from ours, and perhaps we should correct our sifrei Torah to match. (See here where this idea was discussed, and rejected, on parshablog last.) Rashi indeed gets it from a Sifrei, which means that this traces all the way back to Chazal. The pasuk, in Devarim 1:13, reads:

יג הָבוּ לָכֶם אֲנָשִׁים חֲכָמִים וּנְבֹנִים, וִידֻעִים--לְשִׁבְטֵיכֶם; וַאֲשִׂימֵם, בְּרָאשֵׁיכֶם.

13 Get you, from each one of your tribes, wise men, and understanding, and full of knowledge, and I will make them heads over you.'

Rashi writes:

[The word] וַאֲשִׂמֵם lacks a י [after the שׂ; our editions, however, have it]: This teaches us that Israel’s transgressions (אָשָׁם) are hung over the heads of their judges, since they [the judges] should have prevented them [from sinning], and directed them along the right path (Sifrei).		ואשמם: חסר יו"ד, למד שאשמותיהם של ישראל תלויות בראשי דייניהם, שהיה להם למחות ולכוון אותם לדרך הישרה:

So Rashi speaks of a missing yud, while we have it! We could explore what the various supercommentaries do with this, and what is present in the masoretic notes and commentaries. Perhaps later. I want to focus on two things. First, what very old and established manuscripts have here, and on Wolf Heidenheim's explanation which eliminates the question entirely, and quite effectively in my opinion. Even though in the end I don't think I agree with him.

The Leningrad Codex has it malei yud:

1:13 הָב֣וּ לָ֠כֶם אֲנָשִׁ֨ים חֲכָמִ֧ים וּנְבֹנִ֛ים וִידֻעִ֖ים לְשִׁבְטֵיכֶ֑ם וַאֲשִׂימֵ֖ם בְּרָאשֵׁיכֶֽם׃

So does the Samaritan Torah. So our Masoretic text certainly is well established, and has company. If the text in Rashi's Torah happened to be chaser, then so be it, but that does not mean that we must start emending all our sifrei Torah. In the Sifrei, we have

ד׳׳א ואשימם בראשיכם אם שמרתם את (דבריכם) הרי ראשיכם שמורים • ואם לא (שמרתם את עצמכם) אין ראשיכם שמורים מלמד שאשמותיהם של ישראל תלויים בראשי דייניהם • וכה״א (יחזקאל ג) בן אדם צופה נתתיך לבית ישראל ושמעת מפי דבר והזהרת אותם ממני וגו׳ • (סיפ) :ש

where the derasha is made but with malei yud in the citation of the pasuk, and no mention of ketiv or krei.

However, Wolf Heidenheim (we will see inside later) traces this back not to Sifrei but to Devarim Rabba and yalkut shimoni in the pasuk in yechezkel. In midrash rabba, we have:

ואשימם בראשיכם
ואשמם כתיב,
אר' יהושע בן לוי:
אמר להן משה: אם אי אתם נשמעים להם, אשמה תלוי בראשיכם.

למה הדבר דומה?
לנחש הזה שאמר הזנב לראש: עד מתי אתה מתהלך תחילה, אני אלך תחילה!
אמר לו: לך! הלך ומצא גומא של מים והשליכו לתוכה.
מצא אש והשליכו לתוכו.
מצא קוצים והשליכו לתוכן.

מי גרם לו?
על שהלך הראש אחר הזנב.
כך כשקטנים נשמעים לגדולים, הם גוזרים לפני המקום והוא עושה, ובשעה שהגדולים מהלכין אחר הקטנים, נופלים לאחר פניהם.

דבר אחר:
אמר רבי הושעיא:
למה הדבר דומה?
לכלה, שהיתה עומדת בתוך חופתה ונתפחמו ידיה.
אם מקנחת היא אותם בכותל, הכותל מתפחם וידיה אין מתנקות.
ואם בפסיפס, הפסיפס מתפחם וידיה אין מתנקות.
ואם מקנחת היא בשערה, שערה היא מתנאה וידיה מתנקות.
כך בשעה שישראל שומעין לגדוליהם ואין גדולים עושים צרכיהם, אשמה תלוי בראשם של גדולים, ואם לאו, תלוי בראשיהן של עצמם.

But Devarim Rabba is from ~900s or so. And it does not explicitly say that it is chaser yud, but does say that it is ketiv like that, which to me conveys the same thing. But see what Heidenheim has -- ואשימים כתיב, with the yud present, and see what he does with it. In Yalkut Shimoni on Yechezkel:

ואשב שם שבעת ימים (כתוב ברמז שכ"ט). בן אדם צופה נתתיך וגו' באמרי לרשע. הה"ד ואשימם בראשיכם אם שמרתם את התורה הרי ראשיכם שמורים ואם לאו אינם שמורים מלמד שאשמיהם של ישראל תלויין בראשי דייניהם

Wolf Heidenheim, in his supercommentary on Rashi, offers an interesting explanation. He says to know that this statement is based in Midrash Rabba and in Yalkut Shimoni on Yechezkel, and in both these places it does not have the language of chaser yud. Rather ואשימם כתיב. And this girsa is correct, because it is malei yud.

And he offers a grammatical analysis of what the purpose of the derasha is, that it is being read as ואאשימם, but then with the aleph dropping out because of the run of two in a row. It is still different from what we have in the pasuk because it is a shin rather than a sin.

Then, he notes an astonishing thing. Chizkuni notes that in his girsa it says that it is chaser aleph! But that this makes no sense, and so we should change it to chaser yud, even though our texts do not have a chaser yud! We will return to this Chizkuni in a moment, but the conclusion is that Chizkuni regards this as a shibush and emends the text to what we have. Heidenheim continues that he, to, found manuscripts which had in Rashi that it was chaser aleph. And that based on what he wrote, this is all well and good, that an aleph dropped out.

I don't like it so much. Even though he makes a compelling case. Because Rashi says:

ואשמם: חסר יו"ד, למד שאשמותיהם של ישראל תלויות בראשי דייניהם, שהיה להם למחות ולכוון אותם לדרך הישרה:

Following up that it is chaser with the word melamed informs me that he is trying to base the derasha on a feature present in the Biblical text, which teaches us this. But it would not be out of the ordinary for there not to be two alephs there. Indeed, only according to the derasha should there perhaps have been to alephs there initially, so its absence here cannot and should not teach us anything.

Let us turn to the aforementioned Chizkuni. He is gores chaser yud, that is חסר י"וד. And the scribes saw initially in Rashi's commentary just יו with a dot on the vav, in order to complete the word (yud). And they thought that it was an א, and from that day, they began to write chaser aleph.

I think I agree with Chizkuni's explanation of the scribal error, rather than with Heidenheim's support of it.

Finally, we can see Minchas Shai address this, to the right.

I am not going to summarize Minchat Shai, except to note that he gives us a lot to look up. We should really examine the Baal Haturim, for example.

Rather than discuss Minchas Shai, I will give my own tentative conclusions. I believe that Wolf Heidenheim is at least partially correct, in terms of the derashot. Since it says ketiv and not chaser in Midrash Rabba, and in Sifrei it cites the pasuk as malei before giving the derash, I would assert that the pasuk is just as we have it, malei yud, even in front of the author of the midrash. The business with the ketiv is only that the shin with no dot can be read either as a shin or a sin, so they are saying ketiv in order to darshen it as a shin, in order to connote guilt.

I am not convinced that Rashi has a Torah which was chaser either. Rather, Rashi the pashtan channels a whole lot of derash. And his previous two comments were based on Sifrei. And the Sifrei has connections to the Midrash Rabba in terms of derasha. And it is quite possible that in Midrash Rabba, and perhaps even in Rashi's version of the Sifrei, they wrote it chaser. Indeed, in our Midrash Rabba it says ואשמם כתיב. But maybe it should have said ואשימם כתיב as Heidenheim has it. This convinced Rashi that the word was written in front of the midrashic authors as chaser yud, and he took this as the basis for the derasha. Then, either without checking his own sefer Torah, or checking it and not caring for the difference, because his purpose here is to interpret the text al pi the Sifrei, he brought down and explained the basis for the derasha. That it does not match our Sifrei Torah (or perhaps even Rashi's) is beside the point. But Chizkuni, I think, is correct that it should real chaser yud rather than chaser aleph.

And we should certainly not consider changing our Biblical text on the basis of this derasha, even if we would consider doing it in other instances.