It's not just the accuracy of the price data that is the issue.
Good ASX data should have all official ASX dilution factors and corporate actions applied to the database automatically. Dilution factors arise due to various corporate events (stock splits, consolidations, rights issues, demergers, mergers, capital returns etc).
In addition, the data also needs to be fully adjusted for delisting, name changes, code changes, merging of deferred settelment periods etc.
There are around 300 dilutions per year and around 150 code changes per year on the ASX. Given there are around 2100 equities traded on the ASX it's crucial that these corporate actions are applied diligently as you'll rapidly have an inaccurate view of the market.
If your data vendor doesn't do all of the above for you, caveat emptor. Your database will have a lot of useless data. Yahoo does not do all of the above.
Some recent examples corporate actions where Yahoo is defective:
DWY changed code to NYO
Yahoo shows DWY.AX and NYO.AX both as valid codes. Therefore this item is now duplicated in your database.
QOL changed code to QOLDA (due to 10:1 consolidation) then changed code to PMQ. Yahoo's PMQ.AX is missing the trades when it was trading as QOLDA (eg. on 15/16/17 Sept are showing as zero volume yet there were trades on that day)
AWB had a renounceable issue of shares at $1 (exdate 25 September 2009). There is no adjustment for this on Yahoo yet this is a significant dilutionary event.
Trojan equity had a capital return of $0.33 per share (they were trading at $0.75). Yahoo has not made any adjustment for this significant event yet your cost base would have been reduced by 33c.
Telstra history in Yahoo only goes back to 2003. It should show the time when it was TLSCA and TLSCB too (i.e. all the way back to 1998) - Yahoo is missing a significant part of the data!
You need to make your own informed decision as to whether such deficiencies in maintenance, accuracy, corporate actions and dilutions will affect your analysis.