we can use the pd.to_datetime and use errors='coerce' to parse the dates in steps.
assuming your column is called date
s = pd.to_datetime(df['date'],errors='coerce',format='%Y-%m-%d')
s = s.fillna(pd.to_datetime(df['date'],format='%Y%m',errors='coerce'))
df['date_fixed'] = s
print(df)
date date_fixed
0 2001-12-25 2001-12-25
1 2002-9-27 2002-09-27
2 2001-2-24 2001-02-24
3 2001-5-3 2001-05-03
4 200510 2005-10-01
5 20078 2007-08-01
In steps,
first we cast the regular datetimes to a new series called s
s = pd.to_datetime(df['date'],errors='coerce',format='%Y-%m-%d')
print(s)
0 2001-12-25
1 2002-09-27
2 2001-02-24
3 2001-05-03
4 NaT
5 NaT
Name: date, dtype: datetime64[ns]
as you can can see we have two NaT which are null datetime values in our series, these correspond with your datetimes which are missing a day,
we then reapply the same datetime method but with the opposite format, and apply those to the missing values of s
s = s.fillna(pd.to_datetime(df['date'],format='%Y%m',errors='coerce'))
print(s)
0 2001-12-25
1 2002-09-27
2 2001-02-24
3 2001-05-03
4 2005-10-01
5 2007-08-01
then we re-assign to your dataframe.