To expand on quote from OP about
But what is paradise? It is a modern word: it does not answer at all
to the original word that Jesus made use of. Find the original of the
word paradise.
you could look at the biblical hermeneutics question on this word, where the top answer states
meaning is somewhat more cloudy
The quote in OP can also be found in Gospel Topics: Paradise where it gives some more explanation:
A second use of the word paradise is found in Luke’s account of the Savior’s Crucifixion. When Jesus was on the cross, a thief who also was being crucified said, “Lord, remember me when thou comest into thy kingdom.” The Lord replied, “Verily I say unto thee, To day shalt thou be with me in paradise.” The Prophet Joseph Smith explained that this is a mistranslation; the Lord actually said that the thief would be with Him in the world of spirits.
The word paradise also sometimes refers to the celestial kingdom. In the tenth article of faith, the word paradisiacal describes the earth’s glory in the Millennium.
As members of the Church of Jesus Christ of Latter-day Saints believe in the plan of Salvation, this isn't much of a mis-translation. The earlier paragraph from the above article states:
In the scriptures, the word paradise is used in different ways. First, as mentioned above, it designates a place of peace and happiness in the postmortal spirit world, reserved for those who have been baptized and who have remained faithful. Those in spirit prison have the opportunity to learn the gospel of Jesus Christ, repent of their sins, and receive the ordinances of baptism and confirmation through the work we do in temples. If they accept the gospel and their temple work has been done, they may enter paradise.
As LDS believe Jesus started the missionary work1 in the spirit world, Luke 23:43 with the change mentioned by Joseph Smith
43 And Jesus said unto him, Verily I say unto thee, To day shalt thou be with me in [the world of spirits].
Just becomes another verse eluding to Jesus teaching those in the spirit world (spirit prison). Both would be in the spirit world, having died. The two states (paradise/prison) of the spirit world isn't clear if there is an actual physical division, or if it's like here on earth where you can have believers/not all mixed but in different states of mind/salvation.
If scripture/statements are made in error it would be up a prophet to reveal the truth, or someone else speaking with authority (this could be any priesthood holder given the keys(authority) to do so). A quick example is from Alma 11:34-37 where the Alma's companion Amulek is discussing the topic "saving one in sin":
34 And Zeezrom said again: Shall he save his people in their sins? And Amulek answered and said unto him: I say unto you he shall not, for it is impossible for him to deny his word.
35 Now Zeezrom said unto the people: See that ye remember these things; for he said there is but one God; yet he saith that the Son of God shall come, but he shall not save his people—as though he had authority to command God.
36 Now Amulek saith again unto him: Behold thou hast lied, for thou sayest that I spake as though I had authority to command God because I said he shall not save his people in their sins.
37 And I say unto you again that he cannot save them in their sins; for I cannot deny his word, and he hath said that no unclean thing can inherit the kingdom of heaven; therefore, how can ye be saved, except ye inherit the kingdom of heaven? Therefore, ye cannot be saved in your sins.
(Opinion/speculation)Quick note as the New Testament doesn't include a full account of every action of the apostles or other of Jesus' followers, it is possible that the thief was baptized shortly after at some point (Jesus specifically talked to him before dying about being with him in the spirit world in front of his followers (it was recorded), and was later resurrected and visited his apostles, in John 20:30-31 maybe this person was brought up? Again this is speculation, but there are details that aren't included in scripture) As noted in this question it is possible that the thief had already been baptized and just needed to repent and he'd be with Jesus in spirit world and in paradise. Lots of unknowns.
This is also might be a good time to add that my statements do not constitute official statements by The Church of Jesus Christ of Latter-day Saints. It's been expressed previously that you do not like this statement, but even apostles have made statements, they believed in, taught, and/or published, but did not represent the official Church of Jesus Christ stance (Orson Pratt see this answer, Brigham Young see Journal of Discourses, etc). Agency and revelation are key principles of the gospel. I'll state Articles of Faith 9 & 11:
9 We believe all that God has revealed, all that He does now reveal, and we believe that He will yet reveal many great and important things pertaining to the Kingdom of God.
11 We claim the privilege of worshiping Almighty God according to the dictates of our own conscience, and allow all men the same privilege, let them worship how, where, or what they may.
To close, from Elder Dieter F Uchtdorf The Reflection in the Water:
Those who reject revelation and insist on tangible evidence can only speculate or deny that there is life before or after this mortal sphere.
In regards to Joseph Smith not knowing Greek, as a prophet I don't feel like he needed to know Greek to declare something a mis-translation as that can be done with revelation from an all-knowing God. However he did know Greek, see Joseph Smith's Awareness of Greek and Latin
Emphasis mine
1 1 Peter 3:19, Teachings of Brigham Young chapter 38, The Savior's Visit to the Spirit World, Elder Spencer J. Condie