"The Rash sided with the opponents of the Rambam in their disputes." and "reproached Rambam for not having indicated the Talmudic sources in his Mishna Torah" - possibly a reference to one of the letters Rabbeinu Shimshon sent to the Ramah on the subject of the Rambam dispute. In this letter, the Rash rebukes the Rambam for not checking his sources, but rather trusting his memory. For example, here:
"ועל רוב חכמתו סמך ואגב חורפיה לא עיין בה ונעלמה ממנו הלכה זו ופתרונה וכל מה שפתר בה..."
Translation: "...and he trusted his great wisdom and because of his sharpness he didn't examine it and this halacha escaped him and its solution and all that he solved in it..."
"וכמה לא חלי ולא הרגיש האי גברא רבא שבטח בלבו להתיר דבר גדול (כזה) בלא ראיה מסברא, ואפילו סברא אין כאן כלל..."
Translation: "...and how much he didn't fear and didn't feel that great man who trusted his heart to allow such a great thing without a basis from a logical argument, and there isn't even a logical argument here at all..."
These two quotes are examples of beginnings of replies of the Rash to questions sent by the sages of Lunèl to the Rambam; the rest of each of the replies are dedicated to explaining why the sages of Lunèl rightly questioned the Rambam because he was going against the gemara in his psakim.
"condemned Rambams' rationalistic views on bodily resurrection and Talmudic haggadah - In the same letter he wrote:
"וכתב הרמב"ם (ז"ל) בספר מדעי בהלכות תשובה בפרק שמיני - הרמ"ה השיבו בזה - העולם הבא אין בו לא גוף ולא גויה...עכ"ל. ומתוך דבריו נכר שלא עיין בספר שכתב (ממנו שאין שם ולא שתיה) ולא תשמיש ח"ו לא הזכירו תשמיש בדבריהם וסמך הרב על [רוב] חכמתו, ובצדו תשובתו: דאגב חורפיה לא עיין בה. ועיקר מילתא דאייתי מינה ראיה היא שנויה בסוף פרק היה קורא, והכי איתא התם מרגלא בפומיה דרב העוה"ב אין בו לא אכילה ולא שתיה...שנאמר ויחזו את האלהים ויאכלו וישתו. והשתא למה ליה לאתויי [הא] (קרא) דויאכלו וישתו ש"מ דיש גוף של בשר לעוה"ב וזיו השכינה משביעם כאכילה ושתיה..."
Translation: "And the Rambam z"l in the Sefer Mada'i in Hilchot Teshuvah in the eighth chapter wrote - the Ramah replied to him about this - The World to Come harbors neither body nor aught of a concrete form...until here his words. And from his words it is evident that he didn't look into the book, that he wrote (from him that there isn't there drinking) "and no family life", chas v'shalom they didn't mention family life in their words and the Rav trusted his great wisdom and next to that his answer: And because of his sharpness he didn't examine it. The main thing from which is brought evidence is what is written in the end of Ch. Hayah Koreh, and so it says there Rav was wont to say:
The World-to-Come is not like this world. In the World-to-Come there is no eating, no drinking...as it is stated: “And they beheld God, and they ate and drank”, and now, why would he bring the verse of "and they ate and drank"? From here we see that there is a body of flesh in The World-To-Come and the splendor of the Divine Presence fills them like eating and drinking."
"he did express his great admiration for the Rambam saying, "I have heard that the gates of wisdom have been revealed to him"" - This is a reference to the end of the letter:
"ומי כהחכם יודע פשר, כי נמרצו אמרי יושר...ולא להשיב את הארי הגדול אחר מיתה באתי הרב משה אשכול הכופר ממנו פנה ממנו יחד שמענו שמעו כי נגלו [לו] שערי בינה..."
Translation: "And who like the wise man who knows the meaning of things, for honest words were trenchant...and not to answer the great lion after [his] death came I...The Rav Moshe the spray of henna blooms came from him, from him together we heard his teachings for to him appeared the gates of wisdom..."