try this
-----
DECLARE @teamID INT
SET @teamID=23
SELECT t1.name AS Team1, s1.score AS MyScore, t2.name as Team2, s2.score
FROM score s1
INNER JOIN t1 ON s1.tid_FK1 = t1.tid
INNER JOIN score s2 ON s1.date=s2.date AND s1.tid_FK1 = s2.tid_FK2 AND s1.tid_FK2 = s2.tid_FK1
INNER JOIN t2 ON s1.tid_FK2 = t2.tid
WHERE s1.tid_FK1 = @teamID
UNION
SELECT t1.name AS Team1, s1.score AS MyScore, t2.name as Team2, s2.score
FROM score s1
INNER JOIN t1 ON s1.tid_FK2 = t1.tid
INNER JOIN score s2 ON s1.date=s2.date AND s1.tid_FK1 = s2.tid_FK2 AND s1.tid_FK2 = s2.tid_FK1
INNER JOIN t2 ON s1.tid_FK1 = t2.tid
WHERE s1.tid_FK2 = @teamID
------
(SELECT s.score as myscore,s.teamID_FK as me,s.opp_teamID_FK as them from score s where s.teamID_FK=23)
UNION
(SELECT t.score as theirscore,t.opp_teamID_FK as me,t.teamID_FK as them from score t where t.opp_teamID_FK=23)
yields:
myscore me them
1770 23 25
1210 23 30
2080 23 29
1970 23 25
1650 23 30
900 23 29
theirscore doesn't even appear!