Is there any text in the Torah or Mishnah that sees a convert as some kind of "imitation" Jew or someone who isn't as good as a real-deal matrilineal Jew?
A ger tzedek is a very great thing and there's nothing negative about it. One of the greatest Jewish scholars, Onkelos, was a convert. His translation of the Torah into Aramaic is printed in most chumashim.
It's a very negative thing if someone converts insincerely or for ulterior motives, marriage is a very common reason. As Shalom answered " The Talmud does say that "converts are as troublesome for mainstream Jews as a skin disease." " I recall this gemara, although I'm not so sure if it said skin disease, or something else similar. An example of this is Shlomo Hamelech's wives, who converted insincerely and cause a lot of trouble.
The Talmud does say that "converts are as troublesome for mainstream Jews as a skin disease." The commentaries suggest two interpretations: an insincere convert causes problems if s/he keeps missing the family Christmas party etc.; or a truly sincere convert puts the Jewish mainstream to shame because s/he does such a better job keeping the laws!
Also, the mishna at the end of Horiyot talks about some theoretical orders of precedence for honors, e.g. Kohen before Levite etc., and in that order, born-Jew precedes convert; however, the next line insists that this would only apply if all else were equal (which it never is); a scholar who was conceived in an adulterous mess takes precedence over an ignoramus who happens to be the high priest.
There is a rabbinic text which refers to conversion status as being a blemish, but the very same text indicates that a convert is not any different than anyone else in this regard -
Bava Metzia 59b:
מאי דכתיב: 'וגר לא תונה ולא תלחצנו כי גרים הייתם בארץ מצרים' - רבי נתן אומר: מום שבך אל תאמר לחברך
What is the meaning of that which is written "And a stranger do not mistreat or pressure, for you were strangers in the land of Egypt"? Rebbi Nosson says: The blemish that you yourself have, do not point out in your fellow.
The Talmud refers to being a "גר" as a blemish, but points that we all have this blemish, convert and born-Jew alike. The Talmud is clear we are all on the same plane in that regard.
In pesachim it says that a group eating a pesach offering should not be composed of only converts lest they scrutinize the offering and, in their ignorance, find a blemish and mistakenly disqualify their offering.