As stated in the previous answer, any system which shows you the names of the spouses on the same page can only be as accurate or as complete as the indexes themselves are. If the transcribers cannot read the reference on the printed index page, the marriage finder will not be accurate.
A simple way to check the results is to perform the same search on another site which offers a similar feature.
For an example, I'll search for the marriage in 1841 in Sheffield for the couple George Hindley and Hannah Drake, whom I've mentioned in previous questions. All the sites below offer the user the ability to click through and view images of the original index books -- for clarity, I have removed the references to those features from these transcriptions.
FreeBMD gives two results for marriages with spouses Hindley and Drake in the West Riding of Yorkshire. This is the one I'm interested in:
Surname First name(s) District Vol Page
Marriages Sep 1841 (>99%)
HINDLEY George Sheffield 22 448
Clicking on the page link gives the following list of people who have the same index entry and are presumably on the same register page. Here we see that the two transcribers have slightly different readings for one of the entries.
Surname First name(s) District Vol Page Marriages Sep 1841
CLIFF Ann Spuckman Sheffield 22 448
CLIFT Ann Spuckman Sheffield 22 448
DOLMAN Elizabeth Sheffield 22 448
DRAKE Hannah Sheffield 22 448
GLOSSOP John Sheffield 22 448
HINDLEY George Sheffield 22 448
HORNER Henry Sheffield 22 448
Ancestry's data (provided to them by FreeBMD) shows this on the 'record' page:
Name: George Hindley
Registration Year: 1841
Registration Quarter: Jul-Aug-Sep
Registration district: Sheffield
Inferred County: Yorkshire West Riding
Records on Page:
Ann Spuckman Clift
As far as I know, Find My Past does not have a 'tool' whereby you can enter the Registration district name along with the year, volume and page number. They show the results as a banner across their transcription page. For my George Hindley search, the MarriageFinder banner says:
GEORGE HINDLEY married one of these people
HANNAH DRAKE, ELIZABETH DOLMAN, ANN SPUCKMAN CLIFF
The Genealogist's feature requires you to click an icon to find the spouses on the same page. Like Find My Past, they strip out the groom's names and show only the brides if you start with the groom, and show only potential grooms if you start with the bride.
That being said -- your question 'How accurate is this MarriageFinder?' hides some hidden assumptions, which I'll make explicit here.
We've all gleaned information from indexes when we don't have access to the original records -- and in some cases of record loss, it may be that the index is all we have. But the GRO indexes are not original historical source records -- they are a finding aid. We can 'look forward' in time and try to find couples in other records, like the census, to guess which groom and bride belong to each other, but it is still only a guess. We also assume that the record set will have our couple in it, and that the record set is complete. These things may not be true. Note that FreeBMD has this warning on the results page, along with a link to their coverage table.
FreeBMD hasn't yet transcribed the whole index
It's also possible that the couple you're looking for did not marry in the time and place you assumed they did.
Let's take a look at a different couple, starting with the bride shown in this registration found on FamilySearch: https://familysearch.org/ark:/61903/1:1:2D3T-448
Mary Ann Coyde
England and Wales Marriage Registration Index
Name Mary Ann Coyde
Event Type Marriage
Registration Quarter Jul-Aug-Sep
Registration Year 1851
Registration District Totnes
Event Place Totnes, Devon, England
Line Number 36
Mary Ann Coyde probably married one of the following people
Name Henry Fellew
Name Sophia Holman
Name Robert Emanuel Matthews Knowles
Name Ann Lake
Name George Loye
Name Elizabeth Rowden
Name William Trace
A researcher cited this registration as evidence for a nearby Knowles-Coyde marriage.
The parish registers for Brixham All Saints, which is in the Totnes Registration District, are on Find My Past. When I looked at the original registers, I found that the first page of the book had a marriage for Robert Emanuel Matthews Knowles and Elizabeth Rowden, and a marriage for George Loye and Mary Ann Coyde. On the second page of that register book, we see the marriage of William Trace and Sophia Holman. The remaining couple in this list, Henry Fellew and Ann Lake, appear on the last page of the previous volume from Brixham All-Saints.
The marriage the other researcher was looking for took place in April of 1832, so it wouldn't have appeared in the civil registrations at all, but if that couple had married in the same parish after the start of civil registration, their marriage would have been registered in Kingsbridge Registration District.
Looking at the index pages alone can only take us so far. There is no substitute for looking at the original registers.
See Best Practices for Reliable Research and
QuickLesson 17: The Evidence Analysis Process Map at the Evidence Explained website to learn more.
For finding Civil Registrations:
For finding church records once you have the GRO index reference: