If the two totals of a trial balance are equal, dose it mean there is no error in the accounting record?

no , may be the entry is incorrect

no, it is true that it is balance but the entry made is incorrect

The answer is simply ( NO ) , any single balance may be wrongly recorded & this error is included in another single balance(s) but you can see equal totals at the end.

 NO NEVER IF TRIAL BALANCE TALLY MEANS NOT ACCOUNT CLEAR- IF EXAMPLE GOODS PURCHASE FROM x FOR 10  WE ARE ACCOUNTING THIS TRANSACTION LIKE THIS BELOW

X A/C DR

PURCHASE A/C CR

THIS IS ABSOLUTELY A/C PRINCIPLE WRONG BUT TRIAL BALANCE WILL TALLY BUT ACTUAL ENTRY ABOVE THAT IS

PUR A/C DR AND

  X A/C CR

No That is not an indication that no errors in the recording,

NO. IF THE CAPITAL EXPENSE TREAT AS REVENUE EXPENSE, IT DON'T FIND OUT