The disagreements over this spread are not beginners misunderstanding it. They are genuine, they are old, and they go back to ambiguities in the earliest printed description.
Above and below, or future and past
Waite's original description locates cards by physical position, what is above the querent, what is beneath them, what is behind and what is before.
Later handbooks converted those into temporal positions: past, future, foundation, near future. The conversion is not neutral. What is beneath a situation and what is in its past are different questions, and a reader following one scheme will read the same card differently from a reader following the other.
Most modern decks ship with the temporal reading. The positional reading is the older one.
Which way the staff runs
Waite lays the staff of four cards from the bottom upward, ending at the outcome. Some traditions run it top down. Since the four positions are in a fixed sequence ending at the outcome, reversing the direction reverses which position the outcome occupies.
This is why published Celtic Cross diagrams do not agree on which card is number ten and where it sits.
The crossing card
Position two is laid across position one, and Waite is explicit that it is read upright regardless of orientation, because a card laid sideways has no meaningful upright or reversed state.
Many readers ignore this and read the crossing card reversed if it comes out that way. There is no strong argument for it beyond habit.
There is also a persistent question about whether the crossing card is an obstacle or simply the other force in play. Waite's sense is closer to the second, what crosses the matter, for good or ill, and reading it as automatically adverse loses the cases where the crossing card is the help arriving.
Hopes and fears
Position nine is traditionally hopes and fears together, which strikes most people as evasive until they have used it for a while.
The defence is that hopes and fears about the same outcome are frequently the same thing, and that a querent who cannot tell which one a card is describing has usually learned the most useful thing in the reading. The critique is that it makes the position unfalsifiable.
Both are fair. Some readers split it into two positions and run an eleven-card spread.
The significator
Waite places a significator card, chosen to represent the querent, on the table first, with card one laid on top of it.
Almost nobody does this now. It removes a card from the deck before the reading, which most modern readers dislike, and it requires choosing a court card for the querent by a scheme of age, colouring and sex that has not aged well.
Its disappearance is the largest single difference between the spread as Waite printed it and the spread as it is used today.